CIHM 
Microfiche 


(IMonographs) 


ICMH 

Collection  de 
microfiches 
(monographles) 


Canadian  Institute  for  Historical  Microreproductions  /  Institut  canadien  de  microreproductlons  historiques 


Technical  and  Bibliographic  Notes  /  Notes  techniques  et  bibliographiques 


The  Institute  has  attempted  to  obtain  the  best  original 
copy  available  for  filming.  Features  of  this  copy  which 
may  be  bibliographicaily  unique,  which  may  alter  any  of 
the  images  in  the  reproduction,  or  which  may 
significantly  change  the  usual  method  of  filming  are 
checked  below. 


n 


Coloured  covers  / 
Couverture  de  couleur 


□    Covers  damaged  / 
Couverture  endommag^e 

□    Covers  restored  and/or  laminated  / 
Couverture  restaur§e  et/ou  pellicul6e 

I I    Cover  title  missing  /  Le  titre  de  couverture  manque 

I I    Coloured  maps  /  Cartes  g6ographiques  en  couleur 

I      I    Coloured  ink  (i.e.  other  than  blue  or  black)  / 


Encre  de  couleur  (i.e.  autre  que  bleue  ou  noire) 

Coloured  plates  and/or  illustrations  / 
Planches  et/ou  illustrations  en  couleur 


D 
D 
D 


D 


D 


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Seule  edition  disponible 

Tight  binding  may  cause  shadows  or  distortion  along 
interior  margin  /  La  reliure  serree  peut  causer  de 
i'ombre  ou  de  la  distorsion  le  long  de  la  marge 
int^rieure. 

Blank  leaves  added  during  restorations  may  appear 
within  the  text.  Whenever  possible,  these  have  been 
omitted  from  filming  /  Use  peut  que  certaines  pages 
blanches  ajoutees  lors  d'une  restauration 
apparaissent  dans  le  texte,  mais,  lorsque  ceia  etait 
possible,  ces  pages  n'ont  pas  ete  filmees. 

Additional  comments  / 
Commentaires  supplementaires: 


L'Institut  a  microfilm6  le  meilleur  exemplaire  qu'il  lui  a 
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plaire qui  sont  peut-etre  uniques  du  point  de  vue  bibli- 
ographique,  qui  peuvent  modifier  una  image  reproduite, 
ou  qui  peuvent  exiger  une  modification  dans  la  m6tho- 
de  normale  de  filmage  sont  indiqu6s  ci-dessous. 

I I   Coloured  pages  /  Pages  de  couleur 

I I   Pages  damaged  /  Pages  endommag6es 


n 


Pages  restored  and/or  laminated  / 
Pages  restaur6es  et/ou  pellicul6es 


Q   Pages  discoloured,  stained  or  foxed  / 
Pages  d6color6es,  tachet^es  ou  piquees 

I      I   Pages  detached  /  Pages  d6tach6es 

I  y/j   Showthrough  /  Transparence 

I      I   Quality  of  print  varies  / 


D 
D 


D 


Qualit6  in6gale  de  I'impress;.. 

Includes  supplementary  mait-'.e-  / 
Comprend  du  materiel  suppl^r.T-   :    ^e 

Pages  wholly  or  partially  obscured  by  errata  slips, 
tissues,  etc.,  have  been  refilmed  to  ensure  the  best 
possible  image  /  Les  pages  totalement  ou 
partiellement  obscurcies  par  un  feuillet  d'errata,  une 
pelure,  etc.,  ont  6t6  filmees  a  nouveau  de  fafon  a 
obtenir  la  meilleure  image  possible. 

Opposing  pages  with  varying  colouration  or 
discolourations  are  filmed  twice  to  ensure  the  best 
possible  image  /  Les  pages  s'opposant  ayant  des 
colorations  variables  ou  des  decolorations  sont 
filmees  deux  fois  afin  d'obtenir  la  meilleure  image 
possible. 


This  item  is  filmed  at  the  reduction  ratio  checked  below  / 

Ce  document  est  tilme  au  taux  de  reduction  indiqu^  ci-dessous. 


lOx 

14x 

18x 

22x 

26x 

30x 

4 

12x 

16x 

20x 

24  x 

9Ry 

lOw 

The  copy  filmtd  h«r«  has  b««n  raproducad  thanks 
to  tha  ganarosity  of: 

McMaster  University 
Hamilton,  Ontario 

Tha  imagas  appaaring  hara  ara  tha  bast  quality 
possJbIa  considarjng  tha  condition  and  lagibility 
of  tha  original  copy  and  in  kaaping  with  tha 
filming  contract  spacificationa. 


Original  copias  in  printad  papar  covars  ara  filmad 
baginning  with  tha  front  covar  and  anding  on 
tha  last  paga  with  a  printad  or  illuatratad  improa- 
sion.  or  tha  back  covar  whan  appropriata.  All 
othar  original  copias  ara  filmad  baginning  on  tha 
first  paga  with  a  printad  or  illuatratad  impraa- 
sion.  and  anding  on  tha  laat  paga  with  a  printad 
or  illuatratad  imprassion. 


Tha  last  racordad  frama  on  aach  microflcha 
shall  contain  tha  symbol  — ^  (maaning  "CON- 
TINUED"), or  tha  symbol  ▼  (maaning  "END"), 
whichavar  applias. 


L'axamplaira  filmA  fut  raproduit  grica  i  la 
g^nArositA  da: 


McMaster  University 
Hamilton,  Ontario 


Las  imagas  suivantas  ont  iti  raproduitas  avac  la 
plus  grand  soin.  compta  tanu  da  la  condition  at 
da  la  nattati  da  l'axamplaira  filmA.  at  an 
conformity  avac  laa  conditions  du  contrat  da 
filmaga. 

Laa  axamplairaa  originaux  dont  la  couvartura  an 
papiar  aat  imprimia  sont  filmis  an  commancant 
par  la  pramiar  plat  at  an  tarminant  soit  par  la 
darniira  paga  qui  comporto  una  amprainta 
d'imprassion  ou  d'illustration,  soit  par  la  sacond 
plat,  salon  la  caa.  Tous  las  autras  exampiairas 
originaux  sont  filmis  an  commandant  par  la 
pramiAra  paga  qui  comporta  una  amprainta 
d'impraasion  ou  d'illustration  at  an  tarminant  par 
la  darniira  paga  qui  comporta  una  talla 
amprainta. 

Un  das  symbolas  suivants  apparaltra  sur  la 
darniira  imaga  da  chaqua  microficha.  salon  la 
cas:  la  symbols  •-»•  signifia  "A  SUIVRE",  la 
symbols  ▼  signifia  "FIN". 


Maps,  platas,  charts,  ate,  may  ba  filmad  at 
diffarant  raduction  ratios.  Thosa  too  larga  to  bo 
antiraiy  includad  in  ona  axposura  ara  filmad 
baginning  in  tha  uppar  laft  hand  cornar,  laft  to 
right  and  top  to  bottom,  as  many  framas  as 
roquirad.  Tha  following  diag.rama  illustrata  tha 
mathod: 


Las  cartas   pianchas,  tablaaux.  ate.  pauvant  etre 
filmAs  A  dat  taux  da  reduction  diffArants. 
Lorsqua  la  CiOcumant  ast  trop  grand  pour  atre 
raproduit  an  un  saul  cliche,  il  ast  filmA  i  partir 
da  I'angla  supiriaur  gaucha,  da  gaucha  A  droita. 
at  da  haut  an  bas,  an  pranant  la  nombra 
d'imagaa  nicassaira.  Las  diagrammas  suivants 
illustrant  la  mAthoda. 


1 

2 

3 

1 

2 

3 

4 

5 

6 

MICROCOPY    RESOLUTION    TEST    CHART 

(ANSI  and  ISO  TEST  CHART  No.  2) 


1.0 


I.I 


!.25 


2.8 


1^ 

If  1^ 

!^       14.0 


1.4 


2.5 

12.2 

2.0 
i.8 


A  APPLIED  IM/^GE     I 

^S"^  '6-3   East   Main   Street 

r^S  Roi  r;ester.   Ne*   York        14609       USA 

'-^  (716)    482  -  0300  -  Phone 

^5  (716)   288  -  5989  -  Fax 


CONCRETE  BRIDGES 


AND 


CULVERTS 


FOR  BOTH 
RAILROADS  AXD  inUHWAYS 


BY 

II.  (rRATTAX  TYRRELL 

Ch-il  Eitgiiircr 
Graduate  of   Toronto  I'uivcrsilv 


CIIICACO    AND    NKW    VdKK 

Thk  Mykon  C.  Ci.akk  PiHi.isnixc,  Cd, 


i;.  Lt  F.  N.  Spo.v,  Ltd.,  57  Haymarket 

I'joy 


Copyright  1909 

BY 

H  Grattan  Tyrrell 


ri{Ki  Ad:. 


Hri(l<rcs  of  solid 


Jlll.V  () 


tli( 


niati'rii 


cHiirn'tc  iiic  siii)(.ri(.r  to  those  of 


Tl 


JUiil   have  i\   \ 


K'v  arc  as  pcriiiaricnt  as  st 


one 


ilu<-ts  built   l»v  the  Hoi 


<''<s  <-<)st.     .Masoiii-v  l)ji(h 


:('s  and   a«|ii('- 


sniii.'of  tliciii  in  use.    A  tVw  old  cast 
main,  datinjr  l,j„.|<  ;,  ..cntury  ov  uun-o.  but 


nans  arc  still  stainlii 
brid 


iron 


«'f  the  modern  ones  built  of 

lave  ji  very  limited  existence.    Fort 


bridy 


ami 
•'cs  re- 


a  nujjority 
wi-ou]L,dit  iron  and  steel 


es    Avere 


y  years  ago,  steel 


but  It  is  now  well  I 


i)''Iie\ed  to  be  permanent  struct 


nown  that  thev  do  not 


;ist  lonjrer  than  from  twenty  to  tliirt 


urcs. 


},'cnerallv 


y  years. 


Soli 


<1    concrete    bridge 


wliich    rein  fore  in;,'   metal 

tensile  stresses  in  the  arch  riii?.'   ('out 

soal  ' 


are  su|»erior   to   those   in 
is    re.|uired    for   resisting 


inuous  water- 


K'.ifT  reduces  tlu'  adh(>sion  of  concrete  to  steel  1 

illx.l-;      10')    ,„.,.    ,.,.„t.    ;,,„l    tJ„.    ,.ft-,.,,j     ,,f 


)V 


'so   tends   to   dest 
<  furs  that  crach.s  develop,  sufTiciently  ] 


•ihoeks  and  yi- 
n>y  the   bond.     It   fre- 


t"  ml, Mi!  water,  and  when  water  and  ..., 
llie  reinforcing' metal,  it  is  then  only  a  i 
f'X'c  the  metal  is  d.-stroyed  by  rust! 
An  ohi  Avire  suspension  bridw  that 


arffe 


moisture  reach 
ew  yeai's  be- 


\viis  ex 


xamined  and  reported  on  by  tl 


\v;is  found  that  fail 


recently  failed, 
le  writer,  and  it 


I'll-'  Jind  breaking  of  th 


ure  occurred  because  of  tl 


le  rust- 


e  wire  cables   embedded   i 


»  '"  anchorage.     AVhen  the  bri.lge  was  buil 
'l^'ubtless  considered  that  the  cables  when 

111 


n 


as 


t,  it  w 
painted 


rKF.FA  ('/:. 


cind  «'iiil)t'il(|((l  ill  fniHTi'lc.  wtTt  secure  iij^iiinst  cor- 
nisioii.  Siirticiciil  eiiulion  wms  not  t,-il;en  t<i  cxclud'' 
moisture  from  tlie  jiiiehorjiKcs.  nnd  the  nridge  failed 
as  stilted  above,  liy  llie  rustiiit;  and  l)i-eaking  ot  tlic 
eml)e(ldi'(l  metal.  Il  is  esideiil.  Hiei'etore.  that 
the  most  eiiduriti<r  l)i"id<ri's  are  those  of  solid  masou- 
ry.  whore  tio  metal  is  reijuii-ed. 

Many  (>r  the  larjrest  masonry  hridyfes  built  in  re- 
cent years,  have  m-eh  rinj;s  hiiill  of  solid  conerelo, 
without  reinfor«'iii<r  metal  for  resisting  direct  stress- 
es. Details  of  some  of  these  iire  yixcn  in  Tahle  No. 
I.  Hven  in  arches  with  reinforcemeiit.  the  best  dc- 
sijrners  are  now  proportioniiijr  the  anli  riiijrs.  so  the 
line  of  pressure  foi-  uniform  lojids  will  at  all  times 
fall  within  the  middle  third  of  the  ;M-eh  rinj;,  and 
re(|uire  no  reinforcin*;  for  these  loa«ls. 

Tn  the  Enjrineer's  l*o(d<et-riook.  My.  Trautwino 
makes  the  followin<r  statemenls: — "Nearly  all  tlu) 
s<'ientific  principles  wlii(di  eoiistitute  the  foundation 
of  Civil  Enffineerinjr.  are  susceptible  of  complct*; 
and  satisfactory  explanation  to  any  ])ersoii  who 
I'eally  i)ossesses  only  su(di  knowled^'e  of  arithmetic; 
and  natural  philosophy,  as  is  tau<rht  to  boys  in  pub- 
lic s(diools.  The  little  that  is  beyond  this,  may  safe- 
ly be  intrusted  to  the  savant.  lict  tliciii  work  out 
the  results,  and  <iive  them  to  the  eiiirineer  in  intclli- 
irible  lariprn:i«re.  We  can  afford  to  take  their  word, 
because  !^  di  thin<rs  are  their  specialty.  The  object 
has  been  to  elucidate  in  phiin  En«,'lish,  a  few  ii;.- 
])ortant  elementary  ])rinciples,  which  the  savants 
have   enveloped  in  such  a  haze  of  mystery,  as  to 


PREFACE  V 

iviid.T  piiisiiit  hop.'lfss  to  ajiy  hut  «  cmfirnu'd  nuifli- 
I'liialicijui." 

Scvcnil  complete  and  very  comprolionsiv.'  tr.-ji- 
tis.-  have  already  been  ^vritton,  covering  tlio  mat  he- 
iiiatieal  tlieory  (.f  urches,  and  as  far  as  this  feature 
of  the  subject  is  concerned,  there  is  little  left  t) 
be  desired. 

In  til  •  preparation  of  this  manual,  the  effort  has 
therelore  been  made,  to  as  far  as  possible  eliminate 
iiiathenmtieal   I'ornudae,  and  to  jtresent  the  subject 
ill  the  simplest  possible  nmnner.    Only  such  material 
IS  jriven  as  is  directly  re(|uired   in  the  design  and 
eonstruction  of  ordinary  concrete  or  masonry  arches, 
so  it  will  i)e  unnecessary  for  the  busy  engineer  t(» 
spend  valuable  time  and  thought  in  the  perusal  and 
study  of  obstruse   mathenmtieal   treatises.     ]»racti- 
(•ing  en«riiieers  have  but  little  lime  for  nuithematical 
investigation,   and   generally   iimst  accept  fornuilae 
as  given  to  them  by  others. 

A  real  need  for  this  book  is  believed  to  exist.  ();\  - 
ing  to  tb.e  increased  use  of  concrete  l)ridges. 

The  designs  and  data  tables  for  culverts  and  tres- 
tles are  original  with  the  author,  and  are  here  pre- 
sented for  the  first  time.  They  are  the  result  of 
his  own  practice  in  the  design  and  construction  of 
railroad  structures. 

Tn  the  preparatio     of  this  manual.  I  have  receive.! 
valua])lc  assistance  from  my  wife.  :\raude  K  Tyrrell 
a  graduate  of  the  Chicago  Art  Institute,  ami  cx- 
peneneed  in   architectural   design.     I  am   indebted 
also  to  the   following  gentlemen   for  assistance  as 


VI 


Ph'EF.lCF. 


noted:— To  .luliiis  Kahn  f..r  t 


trestles,   {()  Whitiu'v  W 


wo  views  of  eonerote 


arn-ii,   Areliited.    for  v 


iew8 


<»f     the      proposed      Hudson      Memorijd       Mridge, 
to       Messrs.       Leii     and  Felpite     f(.r     views    and 


drn 


w 


inifs     of    the  Hoekv  Hiver    Hridjre.  to  (J,.,. 
S.   Webster  for  a  plioto{?raph  of  the  Walnut   I 
Mrid< 

illiistratiofis  and  draw 


(•  at  Pliiladeli)hia.  and  to  II.  Hawfrood  for  th. 
injrs  (.f  the  Santa  Ana  Bridge 


1   am  also  indeM..|   to   the   Engineering  News   f 


or 


drawings  of  the  pr.-ix.sed  IIuds(.n  .Alenurrial  Bridge, 
the  Spokane  and  th.-  rjrand  Aveime  Bridges,  and  to 
the  Engineering  Kcc.rd  fur  two  drawings  of  the 
Kocky  iJiver  Brid-o  and  drawing  ut  Edn.ondson 
Avenue  Bridge. 

r        ,        ,„.     .  H.  0.  Tyrrell. 

Evanston.  Illinois. 

November,  lOOO. 


TAULr:  OF  CU.\Ti:\TS. 


I'AKI    I  -J'LAIX  COXCRKTi.; 


AKCIl  liKID     iS. 


C'dnijH 


■-•Itloii 


PaKe 


.\(l 


N.iiiianis   ot    MaMniiy   Coil 


iKirtainty    ui    Ala 


iinii 


'•"iiry    ArcFu-; 


struction. 


IliiiKid   Aril 


us. 


Mtioi)   ot   Siiriiigs 


A'Mitiiunt    I'itr 


il 
R 
C 


"^■iKlit   ut    IJri.ly. 


iM-  aiK 


I   Sp;, 


111. 


rowii     lliickii 


Thick 


iicss  u 


f   L 


nnvii    I'illiug 


10 
11 
11 
1-^ 

r.' 
It 


Spandrels    l<i 


Varit 


Kll 


ip-c 


us  Forms  and  How  to  Dra\V  Tli 


em. 


ulii-CenttTid  Arch.      I  lirce  c 


Multi-C 


I'arahoiic  Arcl 
Hvd 


t-ntinil   Arcli.     l-uc  C 


enters, 
enters. . 


les. 


16 
20 
20 
20 


ros 


Sel 


tatic  and   (leostatic    Arcl 


Kxt 


eetion  of   M„st   Snitahle    I 


les. 


ernal  I.nads  and  J 


orni. 


Matl 
Stahility    K 


orces. 


uniatical    nuory  of  the  Arcli! 


■23 
24 
27 
29 


Ih 


Worl. 


imate  Valnes. 


efpnrenients. 


'"iiij,'    I'nits. 


L; 


ine  of  Res-ist; 


me  o 


f  R. 

'"ii't   of    R 


"Hx-.     I-ull   I.oadin 


33 

34 
3,^> 


sistance.     Partial    Load 


3t> 


npnire 


K'ing 4.f; 


Hetermination  of   Arch'  Thickneis: '. ■  •  •  ■  •  5i» 

'••ickniR   51 

\\aterpr<,onng'  and  '  Drainage.' .' ." H 

I'lteniudiatc    Piers . .  •^- 

A!)iitmint    Piers 
Aliiitn 


53 
54 


K-nts    < 

Finndations         5o 


E 


xpansion 


Snrf 


aco    Finish 


Cost   of    Concrete   Arch    li 


ridges. 


vu 


.58 
60 
60 
63 


«* 


ffi 


VIII 


C'OXTHXTS. 


Dosisn  for  a  .io  ft.  Arch  Bn.iiro  ^T- 

LiicvL'u     i.oailiiiir "•> 

Riquired    Arch    An'.-i ^ 

IntcTiiR'diatc     J'iers.      *'" 

Ahiitnuiit    riiTs. ^p 

Tonte  Kotto.  Rnnu  -Masonry    Urulgcs 71 

Bridge  n{  Augustus  a.  ■Rimini,"  Vtni; Ij 

Hudson  Memorial   Uridge    W-w  York- ■(•;;,■• i? 

A'u-klan.l.   X,.v  Zealand.    P.ridL        ^    -"" '^ 

Rocky  R.vcr  Bridge..  CIcvcIan.lOhiu " "  f ? 

^Valn„t    Lano    Brulgc.    Philade  pi  i"    ?J 

Snmn     \     -"^  p'- r   '^'■"'R^"-    Illinois.  .  .  .^      J' 

San  a   Ana    Hndge.    Cahfornia . .  ^? 

i  able    ot    Lc.icrete    Arch    Bridge^ Jl 

''^''^  "mSufS^^^^^  coxcRETE'ARai 

Historical    ( )ntiim' 100 

Advantages  of   Rdn f^^c^d'  Voncrae !'!; 

Adhesion   and    Bond  106 

Metal    Reinforcement. . .., 1'"^ 

Reinforcing    Systems. HI 

Concrete    Conifx  .sition 1 1" 

Loads   120 

rnits-L-ltimatc  "and"  \\V„-kiV'g |-'! 

1  hcorv  of  Arches  l'2> 

r.ciicral    ntsign     1^8 

Hinged  Arches.        136 

Rililiod    Arches...    NO 

Intrados    Form. .       1-H 

Spandrels !■!•'> 

Piers    and    Ahntments 1-1" 

c™..  ot  _Roi,,f„,c„i  concv;;^  ■  Xr.:,;  nri„„„ :::::::  I  ^  ^  1^5 

Appro.vimatc  J'lstiniating'  ivices V'^ 

1  a  hie   of    Approximate    Ouantitie^ .' .' .' I'J'' 

I  otoniac  ^(enional    Bridge   D-si-n         }. 

.lanv>f,,\vn   Exposition  ISridge.     ^    ',7 

I'rnnkhn  Brid-re,   Foresi    P-,rl-    kV'i       ■ l''l 

TcfTerson   St.    Br id-H-    S  m,  f    P.^  '      T^ '^1 

r.arv,  Indiana.  BJidge  '''  ^"'''■'"■' l''l 

O-imo   p:,rk   Foot   Prrid"-e    St '  P-,,'.! "'-^ 

B,.dde.    Faced    Bridg!^^^^^^^  S 

^1  nn;l    Rapuls    Arch    Bridge  1"» 

^-^ !(]G 


'.  -^'msi^'^^^'^^msm 


COXTF.XTS. 


IX 


T^ridgc  at  V 


I'll  ire. 


Calif 


nartiiM   Park    l',ri<Itji-    C 
Suin-Toiifcn    l',rii|"i.  "s 


Tal>I 


>{  i 


oriiia . . 
'iicay<' 
\vit/cr!a;i(|. 


Page 


xtiiit(,ri\-(l  C.ncn.-tc  .\roIi 


PART  ITI.-IHrjIW.W  HHA 


<>nii)ansnii  ot  ,\rcli  and   li 


M  HRIlXii; 


It;') 
.  Wi) 
.17.{ 

174 


Htani    IWulii 
Mcthud  of  D 


•cam. 


I'Slgl! 


■\RT      ly-COXCRFTE      CLTAT 


.181 
.183 
.18.j 


TKKSTI.i;s 


R'lS 


AX  I) 


cqiurc.l    Si;^f   of    Culvert    On, 
euitorcrd    Concrete    I" 


eiimg. 


Load 


>x    Culvert 


.18!) 
.  1!»1 


I- 


coiU)inK-  i.c'iiKtli   for  Sial 


Reinf 


ii'.s  and  Sial)-1 


orced  C.  m-rete  Slal.  Tal.le   \o.  \-l 


>eanis. 


nRle  Box  Gdv.ns,  Slal.  T;pe.Tal 


I>i)llMe   UnK  Clll 


)Ie  \, 


\'l!, 


ingle   l!,,x  (u! verts/ R 
DouMe  Ho\  C-.dverts.  V, 


vtrts,  Slab  Type,  'ial.ie  X,,',  Vlij 


earn 


Otl 


ler  C 


T'ltne  Ciihert  Co>t.s.  \'ri 


uul  Slali,  Tahle  Xo    IX ' 
am  and  Slal..  Tal.le  Xo.  X..' 


""lion  Culvert  !• 


irious  !• 


I  .rnj-. ....  o 


Culvert  Data.  Tahlc  Xo.   XI 


ornl^^. 


Con 


Crete    Railroad     Trestles  '. -'-' 


.1!)4 
.It).-. 
.I9i< 
.198 
.2(1.'', 
.207 
.209 
Ml 
13 

m 

097 


0 


conomic    Span    Lengths 
'escription  of  Various  Tresile'Dei 
csign    A..  "-^    !'«.. 

B . . .  

C 

n.,..     

K...         

F ;;;; 

G  and  li 


28 


igns. 


.2.30 
.230 
.230 
.235 
.23.5 
.2.38 
.2.38 
.2.38 


oniparative  Trestle  Costs -^? 

242 


LIST  or  /J.J  ISTR.ITIOXS. 


PART  I. 
.     .  Solid  Concrete  Arch  Brihges 

trontispiece-Potomac   Memorial   Bridge,   Washington. 


Pig 
1. 

•1 

4. 
A. 

<j. 

I . 

H. 

!<. 
10. 
11. 
12. 
13. 
14. 
lo. 
Hi. 
17. 
18. 
19. 
20. 

21. 
'>■; 

23! 
24. 


20. 
27. 
2f<. 
2!» 
30. 
31. 
32. 
33. 
34. 
35. 
36. 

37. 
38. 
39. 


21 
22 
23 
26 
27 
■S8 


Ellipse    P^Kf- 

Three   Centered   .Arcli "^ 

Pive  Centered  .Arch 

Parabolic    Arch 

Hydrostatic    Arch ..........'. 

Comparison   of  Above   Curves 

Pressure  Curve,  Full   Loads.    ^ 

Alternate  Pressure  Curve.  Full  Loads.' .' 44 

Pressure   Curve.   Partial   Loads it 

Design  for  Twui  Arches....  To 

Abutments    ^2 

Design  for  Railroad  Bridge ?-!) 

Ponte   Rotto,   Rome "o 

Bridge  of  Augustus  at  Rimini,'  Italy 7^ 

Hudson   Memorial    Bridge  -r 

Monroe  St.  Bridge,  Spokane.  "Vvasli .'.'."".' 70 

Rocky  River  Bridge,  Cleveland ....  L, 

Rocky  Ruer  Bridge,  Cleveland 00 

Rocky  River  Bridge.  Cleveland ....       qa 

Walnut  Lane  Bridge.  Philadelphia at 

Connecticut   Avenue   Bridge.   Washington." .' 88 

Big  Muddy  River  Bridge.  Illinois. .  f 

Santa  Ana  Rrid,q:e,  California  

Santa  Ana  Bridge,  California .".'.'.'.'.". 

PART  II. 
Design   for  Concrete  Higluvav   Bridge  on 

Theory   of    Arches '  ,04 

Grand  Avenue  Bridge  Design,  Milwaukee: .' .' .' 43 

James  own    E.xposition    Bridge..   .  ,Mn 

f/ff^''"  g"''^'''-/:r^t  Park.  St.  Louis.':.',;.:: m 

Jefferson  Street  Bridge.  South  Bend.  Indiana 64 

Gary,   Indiana.   Bridge..  J.". 

Como  Park  Foot  Bridge.  St.  'PauL' : : : : «? 

Boulder  Paced   Bridge.  Washington .  .  laL 

Grand    Rapids   Arch    Bridge . .  }2° 

Bridge  at  Venice,  California  {-, 

Garlield  Park  Bridge.  Chicag.i: ::::::::::: 172 

PART  III. 
Three   Span   Beam   Bridge....  ,o(\ 

Single  Span  Slab  Bridge..         ]fl 

Single  Span  Beam  Bridge. }^ 


l>0 
92 
93 


LIST    OF    ILLUSTRATIONS. 


XI 


Fig. 

4". 

41. 

\1. 

43. 

41. 

4"). 

4i;. 

17. 
1.^. 
1!>. 
•Vt. 

r.i. 

.V2. 
•VI 

.ji. 

■V'(. 

•It;. 

"m  . 

'0, 

til*, 
(ii. 
lii. 
(;:r 

ti'i. 
tit;. 


PART  IV. 

Page. 

Richmond.    Va..    Trestle 18ti 

Augusta,   Ga.,    Trestle 1!)0 

Relative  Cost  of  Slab  and   B.anis •_'()<> 

Single    Box    Culverts.    Slabs -202 

Double    Box    Culverts,    Slabs -joS 

Single   Box   Culverts,    Beams 2(i4 

Culvert    Cost    Chart 213 

Culvert    Cost    Chart 217 

Concrete   Box   Culverts,   Slal)S 218 

Concrete   Box   Culverts,    Beams 22i) 

2eam  Top  Box  Culverts 221 

Concrete  Box  Culverts,  Slab  Type .222 

Concrete  Box  Culverts,  Beam  and  Slal) 223 

Rail  Top  Culverts 224 

Reinforced  Concrete  Arch 22.') 

Beam   Top  Culvert 220 

Paraliolic    .Xrch    Culvert 22(5 

Sewer  T\  pc  .\rch  Culvert 227 

Concrete  Trestle.  Design   .X.  Rail  Top 231 

Concrete  Trestle.  Desifjn  B,   Ream  Top 233 

Concrete  Trestle.  Design  C,   Steel    Beams 234 

Concrete  Trestle,  Design  D,  Beam  Top 236 

Concrete  Trestle,  Design  E.  Slalis  with  Rods 237 

Concrete  Trestle,  Design  F.  Beam  and  Slabs 2.39 

Concrete  Trestle,  Design  G.  Slabs 240 

Concrete  Trestle.  Design  IT,  Beam  and  Slab 241 

Concrete  Trestles,   Comparative   Costs 243 


li 


I 


1 


PART  I. 

PLAIN  CONCRETE   ARCH  BRIDGES. 

Composition. 

Masonry  arclios  vcrc  fontiorly  Diiilt  almost  on- 
tircly  t)f  brick  atid  stone.  In  recent  years,  however, 
owitifi  to  the  increased  prodnction  of  cement  and 
modern  methods  of  making  c»»ncrete.  including  the 
crushing  of  stone  and  the  mixing  and  handling  of 
materials,  a  large  nund)er  of  iiir  modern  bridges  are 
built  of  concrete.  P>rick  andies  hudv  the  bond  of 
stone.  They  a.*e  usually  laid  in  concentric  rings,  the 
I'dge  of  the  brick  appearing  in  the  soffit  of  the  areh. 
()<'('asionany  the  bri(d<s  have  been  laid  dry.  and 
irrout  run  in  to  fill  solid  all  cavities.  As  brick  is 
a  softer  uuiterial  than  stone  or  concrete,  its  use  does 
not  appear  to  have  any  special  advantage.  All 
masonry  arches,  whether  built  of  brick  or  stone  as 
blo(d\  structures,  or  nuule  of  conert-te  in  a  solid 
monolith,  carry  their  loads  entirely  through  com- 
pression in  the  arch  ring,  and  while  the  uiortar 
joints  would  doubtless  resist  considerable  tension  if 
so  re(|ui>-<'d.  no  reliance  slumld  be  placed  on  the  ten- 
sile strength  of  such  joints. 

Advantages  of  Masonry  Construction. 

In  niany  respects  a  masonry  arch  is  sui)erior  t<» 
ritlier  a  steel  l)ridge  or  a  combination  of  steel  and 
concret(\  Some  of  these  advantages  may  be  enu- 
merated as  follows: — Cenu'nt  hardens  with  age.  ami 
co!isefpiently  the  older  the  bridge,  the  stronger  it 
iHM'omes.  Therefore,  if  it  successfully  sustains  its 
first  test  load  it  will  always  be  secure.  This 
condition    is     reversed    in   steel    structures,    which 


^^n 


"^W>JE>i.if 


2  COXCRETi:    BRIDGES   .IM>    ClI.rEKTS. 

(Ictcrioratc  with  aire  llirt>u<rli  the  iictioii  oT 
nisi  and  Ihc  loosciiiiij;  ol"  rivets  and  pins.  As 
travel  increases,  enncrete  l)rid<;es  Ix'conie  stronj^er 
to  support  it;  neither  is  there  any  yearly 
expense  for  paintinj;  or  ntliei  niainti-nance. 
Tliey  ean  <;enerally  he  built  from  l;»eal  nia- 
tei'ial,  and  iarfrely  hy  local  and  unskilled  labor. 
The  buildin*,'  and  completion  of  such  bridges 
is  not  dependent  on  mills,  shops,  or  the  operation 
of  trusts,  as  is  fre<|uently  the  case  with  steel  struc- 
tures. In  this  respect,  concrete  bridjjres  have  an 
advantaire  over  those  of  cond)incd  steel  and  concrete, 
for  in  the  latter  case,  it  is  fre(|uently  necessary  to 
await  the  convenience  of  the  shops  for  the  reinfor- 
cin<^  steel.  A  consideration  that  should  appeal  to 
the  purchasers  of  bridjres  is.  that  local  labc  ■  and  ma- 
terials for  concrete  structures  can  usually  i»e  secured 
and  used,  and  the  money  expended  by  a  miuiicipal- 
ity  <;oes  back  to  its  own  people,  instead  of  j;oin<;  to 
distant  points  in  payment  for  nuinufactured  steel. 

Arches  in  jreneral.  which  form  is  usually  adopted 
for  masonry  bridj^'es.  present  a  more  substantial  and 
!)leasinti  appc  .i'a!ic(-  than  can  ])e  secured  by  any 
foi'm  of  truss,  even  thouj;h  an  andicj  truss  be  con- 
sidered, for  in  a  truss,  the  outline  of  the  arch  is  not 
so  evident  as  in  a  solid  stnicture.  F(>r  railroad 
brid<;es  the  arch  of  solid  concrete  is  superior  to  Ww 
reinforced,  in  that  its  ^'reater  weijrht  and  nuiss  more 
readily  absorb  the  vil)rations  and  shocks  due  to  the 
passajre  of  heavy  traiidoads  and  euf^ines.  Concrete 
bridges  require  no  lioor  renewals  as  steel  bridges 


k 


; 


/7..//.V  coxcRirrii  akcii  briikjus.  :'> 

frcqiicnlly  do.  and  they  will  jr«'iu'rally  cost  from  l'> 
to  :}()  per  ci'iit  less  than  stoiu'.  They  ai-c  tiro  proof 
;iii(l  liav(>  no  sttM'l.  cithor  i.i  the  form  of  priaei|>als  or 
iciiiforcemeiit.  to  rust.  They  can  be  Aviil(  iied  at  rny 
lime  without  tearing;  down  the  orif^'Uial  hridjjes,  as 
mist  he  done  with  brid^'es  of  wood  and  steel. 

I'.ridjres  of  solid  concrete  are  particularly  suitable 
lor  permanent  railroad  structures.  Many  railroad 
coiiipanies  are  roali/.in<?  their  suitclor  advantages 
jiiul  are  replacin<;  their  steel  bridiL^es  with  new  ones 
of  masonry,  and  while  thes<'  concrete  bridges  arc 
fre(|U(>ntly  reinforced  with  steel,  the  main  arches 
are  in  most  cas .s.  designed  to  resist  only  compres- 
Xwv  stresses,  with  no  need  for  steel  in  tension  except 
to  better  utiite  the  arch  and  to  prevent  cracking  from 
change  of  temperature.  .AFany  iron  and  steel  rail- 
road bridges  in  America  have  been  replaced  two  or 
three  times  l)y  licavier  st.'el  ones  during  the  past 
thirty  or  forty  years,  in  order  to  renew  worn  out 
sti'uctures  or  to  provide  for  heavier  loads.  When 
it  is  rcDiembered  that  several  nujsonry  bridges  in 
Europe  that  were  built  2.000  years  ago,  arc  still 
standintr  and  in  use.  it  is  evident  economy  for  per- 
manent roadways,  to  rebuild  ordinary  spans  in  ma- 
sonry. Views  of  two  old  Roman  bridges  are  shown 
on  subsc'iuont  pages.  Ponte  Rotto  at  Rome,  shown 
on  page  73,  was  first  completed  in  the  year  142  B.  C, 
and  while  it  has  been  danuiged  several  times  by 
Hoods,  owing  to  its  unfortunate  location,  three  arch 
snans  still  remain  in  good  condition.  The  Bridge  of 
Aiigustus  at  Rimini,  supposed  to  have  been  built 


"M^^t  m  -jl-A  r-.c-^i; 


4  COXCRE'IL   DRIIKil-S   .IXP   CI  l.rERTS. 

filiout  14  A.  I).,  (lurinp  tlic  n'ifrii  o\'  Kmpcror  Aiifrus- 
lus.  has  five  arcli  spniis.  Tlw  i>i«'rs  an-  very  hoavy 
and  support  scniirivcular  arches.  The  hridfie  is  fine- 
ly onianicntfMl.  is  still  in  -rood  coiidition  and  in  use 
at  the  i)resent  time.    A  view  is  shown  on  papje  75. 

Uncertainty  of  Masonry  Arches. 

As  compared  with  sttM'l  frames,  the  desifjn  of  ma- 
sonry arches  is  uncertain.  The  hypotheses  upon 
whifdi  the  desi<.Mi  is  hascd  are  only  approximate  as- 
sumptions, and  Avhen  constructed,  the  action  of  th" 
andi  under  loads  is  unreliable.  In  the  former  case, 
with  single  truss  systems  and  truss  lines  meetiti-r 
in  points.  Avitii  workin«;  unit  values  (dosely  known 
by  lon<^  series  of  exjierinuMits  in  both  tension  and 
('(•mpression.  the  desi<rnin«r  of  such  frames  has  be- 
come almost  an  exact  science.  It  is  dif^'erent  with 
iiutsonry  andies.  as  their  conditions  under  loads  are 
^oo  little  known  to  arrive  at  any  exact  metho<l  for 
l)roportioninjr  them.  Moreover,  even  if  these  con- 
ditions were  more  lofinitely  known,  the  same  incen- 
tive for  reducing  the  (piantities  of  material  does  n<'t 
exist  in  masonry  as  in  steed  structures.  ])ecause  of 
the  coniparalive  cheapness  of  masonry.  Some  of  the 
indefinite  factors  in  the  design  of  masonry  arches  are 
as  follows : — 

(1)  The  condition  and  amount  of  the  external 
forces  are  n(»t  definitely  known.  For  instance,  ui 
an  andi  with  spandrel  earth  fillinfr.  the  amount  of 
the  conjugate  horizontal  pressure  of  the  earth  against 
the  extrados  of  the  aridi  is  comparatively  unknown. 


•^^^rrs^m 


!'i..ii\  coxcNiiiii  ARCH  BRinans. 


ir   till'   tillinjr  wore   ii   li<ini(l.   the   oxt(>rnal   pressure 
would    then    be    tioniial    to   the    extriuh)s      and      its 
ituouut   would  he  definite.     This  eondition  does  not 
ordinarily  exist,  and  the  nearest  approach  to  liipiid 
pressure  is  from  s|)andrel  tiUin<r  of  (dean  dry  sand, 
it  is  well  known  that  earth  tillinjr.  whicdi.  when  new- 
ly  phi'-ed.  will  stand  at   no  <rreater  slope  than   om- 
iiiid  onedialf  to  one,  will  after  it   heeonies  set.  su|>- 
port  itself  for  a  time,  at  any  rate,  with  alnu)st  verti- 
cal   faces.      Ilenee.    eonjuirate    pi'essure   whi(di    may 
have  existed  at  first,  while  the  andi  was  under  eon- 
^tru(•tion.  may  vanish  hiter.     In  the  case  of  an  arcii 
under  a  deep  embankment,  it  is  plaiidy  evich'iit  that 
such  an  andi  does  not  sui)port  the  entire  wei^dit  of 
earth  fillinjr  above  it.  as  the  earth  to  some  extent 
andies  itself.     The  case  of  a  tunnel  andi  is  an  excel- 
lent   example.      Such    an    andi    is    proportioned    to 
carry   only  a    small   jiart    of  the  load   above   it.  de- 
p('ndin<i-  upon  the  natun'  of  the  overlyinj?  material. 
Further,  where  the  masonry  is  continuous  over  the 
piers,  especially  where  a   l;tr<rt'   amotuit   of  ba(d<inj^ 
is  used,  the  material  tends  to  cantilever  itself  from 
the  piers,  and  thereby  relieve  the  andi  of  miudi  of 
its  load,   or     if  the  amount   of  backing,'  and   filliii'Jr 
above  it  be  lar«re.  these  materials  may  to  a  «rreat  ex- 
tent andi  them.^elves  from  pier  to  pier,    and  thereby 
relieve   the  real   masonry  arch.     The  external  span- 
drel walls  may  also  act  as  arches  and  carry  a  con- 
sideraiile  load.     The  above  remarks  ai)ply  to  liridge 
andies.    In    he  case  of  arches  in  buildinjis,  the  con- 
dition of  the  external  loads  or  forces  is  even  more  iu- 


!  M 


•i    ! 


,     1 


■HKHi 


i;  COXCKlill:    HRIlHiliS   .IXP   CIIAERTS. 

(li'linitf.  Take,  for  fXiiinplc.  tlu'  case  of  aiiarchcar- 
ryiii<r  a  wall  lna<l  a^ov.-  it.  It  is  custoiiiary  to  con- 
sider that  the  arch  carries  the  entire  weight  of  such  a 
wall  The  fact,  however,  is  that  an  unbroken  wall 
supports  itself  almost  etitirely,  hy  actinj;  as  a  mason- 
ry beam  or  hy  archiiijr  itself,  anil  the  only  portion 
snitported  hy  the  arch  is  a  trian«;ular  piece  of  ma- 
sonry directly  above  it.  This  is  true  for  a  wall 
without  ojK'niiijrs.  When  openinjrs  occur  the  above 
consideration  will  be  etlfected.  depending'  upon  the 
location  of  the  openin<rs.  If  they  occur  in  such  i)o- 
sitions  MS  to  evidently  interfere  with,  and  destroy 
tli(  beam  or  arch-action  of  the  suiterimposod  nni- 
sonry.  then  the  entire  wei«rht  of  masonry  may  come 
on  the  arch.  There  are  many  bridfre  arches  now 
standinj;  that  W(»uld  doubtless  fail,  were  they  sub- 
jected to  the  entire  weiy:ht  of  the  materials  above 
them.  After  strikiniL'  center,  the  andi  itself  has  set- 
tled. ;'nd  nnich  of  the  imposed  load  is  transferred  to 
the  piers  by  the  cantile\«  .  or  andi  action,  of  the 
backinir  and  fill,  or  the  arch  action  of  the  spandrel 
walls. 

(2)  Another  unknown  factor  in  the  desi<,Mi  of  ma- 
sonry arches  is  the  strenjrth  of  masonry.  Experi- 
ments have  been  made  ])rincipally  on  small  sam- 
ples tested  in  machines  with  pressures  normal  to 
surface,  all  of  which  c(Miditions  are  (|uite  different 
to  those  of  a'-tual  arches  nmler  loads.  The  material 
is  th(Mi  concentrated  in  l)nlk.  Avith  pressures  inclined 
to  bearing,'  surfaces  and  with  loads  more  or  less  of  a 
vibratory  luiture. 


■\S. 


PI..HX  COXCRliTIi  .IRCII  nRHKir.S. 


it 


(\\)  It  is  usually  assiimcd  by  .'iijriiiccrs  iind  ai 
iilysts.  that  til.'  .joints  ».f  hlock  structures  sui-li  a^ 
masonry  arclu's  ^vill  resist  no  tensile  str.'ss.  This 
is  a  pr'eeaution  on  the  side  of  safety,  hut  may  hi- 
lar from  true.  With  a  rieh  .lualily  of  eoiierete.  we 
know  that  i)roi)erly  formed  points  will  actually  re- 
sist c..nsi(h'rahle  tension.  !)rovided  they  remain  in- 
tact. 

(4}  The  position  of  the  line  td"  resistance  in  the 
arch  is  not  detinitely  known.  This  is  lar<,'.'ly  du.'  to 
the  continuity  of  the  andi  at  the  ceider.  and  the 
sqr.are  heariufrs  at  the  piers  or  spritifrs.  To  obviate 
this  difticulty.  some  European  enjrineers  have  l)udt 
masonry  arches  with  hin«res  at  the  crown  and 
springs!  thus  fixing  the  position  of  the  line  of  resist- 
ance at  these  points,  but  in  America  such  provisions 
are  not  generally  used. 

(."))  Tmi)erfect  workmanship  in  the  cutting  of  the 
stones  and  the  littiiig  of  tlu'  joints  is  another  factor 
.•ausing  the  actual  line  of  resistance  to  m()V(>  from 
its  supposed  position  to  a  different  one.  where  the 
joints  come  to  a  firm  bearing. 

((5)  The  removal  of  the  andi  center  and  the  se^ 
tling  of  the  arch  to  its  pormanent  position,  al  u> 
effects  to  some  extent  the  theoretical  considerations. 
It  appears  therefore  that  any  effort  at  ultra  re- 
finement in  arch  design  is  a  waste  of  energy,  for  the 
actual  conditions  existing  in  a  completed  structure 
niay  not  even  approximate  those  assumed. 


1 


^ 


8        C(>\i'h'i:ii.  nk'ii'ciis  .i\i>  CI  i.n:h''s 

Form. 

Tlif  riinii  or  trt'iicriil  oulliiK'  is  tli<"  iicst  cuiisitli'i'M- 
tioii  ill  the  (|('si<,'ti  t\^  ;i  iiiiisoiiry  jin-li.  Sciiiicir- 
nilnr  jiml  sciiii-i'llipliciil  ;ir<lii's.  i  (»iiimi>iily  kiinwn  as 
full  (M'!il('i-('(1  jiii'lirs.  s|)i-iii«r  from  liorizniitiil  ln-tls, 
uliilf  scjrnit'iitji!  iin-hcs  spi'iiiy:  fmiii  iin-liruMl  ImmIs 
ciillctl  sK('\\  harks.  Tlic  nld  IJoiiiaii  arches  wtTc  iicai'- 
ly  all  sciiiicirtMilar.  In  hridjrt's  and  \iadiii'1s  whci'i 
P'km's  art'  used,  lull  ct'iitcrcd  archts  or  thosf  which 
spriiif;  from  hoi-izontal  hcds.  ai-c  prct'crahlc  lo  sc(»- 
mciital  an-lics  spriii^niijr  t'l-oni  inclined  hcds.  for  \\w 
reason  that  full  centered  arches  prodnce  a  less  over- 
tnrninjr  luonient  on  the  pier,  and  their  attachment 
to  the  i)iers  \vifh  hoi'i/ontal  hcds  is  simpler  than 
with  inclined  sprinijs.  The  thnist  on  piers,  however. 
d(  pends  upon  tlu'  I'ise  of  ai'ch.  which  is  not  neces- 
sarily the  distance  from  sprinjr  to  center  intrados. 
Tlie  c!Vecti\('  rise  is  the  vei'tical  hei<rht  from  sprin;4 
lo  crown,  mi  .isnred  on  the  lineal"  ai'ch  or  line  of 
pressure  and  any  minor  curve  .)o.inin<r  th.'  a''ch  sot'fit 
to  the  pici-.  is  not  ctTective  and  nuist  not  he  con- 
sidered as  part  of  the  ris( .  Se>iiiiental  ai'ches  li.ivo  a 
shorter  curve  than  elliptical  for  the  same  span,  or 
for  the  same  lcn<:'1h  of  soft!',  the  sej^montal  arch 
results  in  a  wider  span.  For  sm:dl  spans  such  as 
conuiionly  used  f«ir  culverts.  se<rinental  ai'ches  con- 
tain from  2.')  to  4n  per  cent  less  masonry  than  senii- 
eircular  nrchos.  thcup-h  common  jtractice  makes  the 
scETmontal  arch  riii<r  10  to  2.")  per  cent  thicker  than 
tl;e  soniicircular.  For  lluid  pressure  the  proper 
form  of  arch  is  the  semicircle.     The  effect  of  earth 


\ 


/7..//.V  cowis'iri:  .INCH  nk'in(;iis.  !• 

fill  or  other  loads  at  tlic  liauticln's.  tftuls  to  raise  the 
line  of  pressure  to  the  appntxiniate  t'oriii  ot"  an  el- 
lips  '.  while  the  efVeet  of  a  unift»riu  l(»a(l.  siieh  as  the 
we.  -lit  of  earth  fill  and  pavement  above  the  crown. 
to<j:eilier  with  a  uniform  live  load,  tends  to  dej)ress 
the  line  of  pressure  to  the  apj)ro.\inuite  form  of  a 
parabola.  The  eomltiJU'd  efl'ect  oi  these  two  loadings 
is  to  briiiir  the  line  of  pressure  more  nearly  to  the 
sej^men*  of  a  eirele.  The  most  economical  form  is 
a  lineal'  arch  >>['  the  <,'iven  span  for  the  reipiired 
loadintr,  in  which  the  thickness  is  proportional  to 
ihe  thrust.  In  such  an  ai-ch  every  part  of  the  cross- 
section  would  be  stressed  alike.  One  authority  ree- 
omnu'Uds  that  the  form  of  intrados  for  an^hes  with 
cai-th  filled  haunches  be  midway  between  a  circular 
sejrment  and  ellipse.  Any  variation  from  re«rular 
curves  that  is  sufVicient  to  be  a[)pareiit  to  the  eye,  U 
a  violation  of  a  principle  of  desijjn  and  should  not 
l)e  permitted.  The  many  three  and  five  centered 
fhit  arches  already  in  existence  are  sufficient  to  ch  r- 
ly  prove  the  utter  failure  of  such  forms  to  produce 
artistic  or  satisfying:  efTeets.  If  multi-centered  flat 
arches  must  be  used,  they  should  be  drawn  from  as 
many  centers  as  possible.  Thre<-  and  five  centered 
arches  are  suitable  when  the  form  approaches  a, 
semicircle. 

An  economical  form  of  arch  with  cantilever  brack- 
ets at  the  ends  has  lately  been  built  over  the  Vermil- 
lion River  at  ^Yakeman,  Oiiio  The  bridge  has  cross 
walls  with  open  spandrels,  a  clear  si)c.n  of  145  feet, 
and  end  cantilever  brackets  37  feet  long.    The  reth- 


"r!».  'LvwH'iMa'rjn 


o( 


ioxcRiiii-  HNiiH.iis  .ixn  cri.riih'Ts. 


1   nc'issitiitcs  llic  use  (if  rcinCon 


<'iiii(»rciii<r  Jiictiil  at  tho 
lt()(.i-  li'vcl  for  tlic  purpose  of  tyiii«,'  the  l)ra('k-('ts  to 
l!it'  iiiaiii  span.  A  sotnewliat  .similar  plan  was  adopt- 
ed in  liie  Topeka  hridtre.  l)ut  in  the  latter  ease  the 
eonerete  cantilevers  were  for  retainin*;  walls  only. 
The  eanlilcvers  were  tied  tojrether  with  rods  to  pre- 
vent spreadin-r  from  the  i)ressnre  of  the  earth  filling. 
In  the  case  of  arches  such  as  culverts  under  high 
end)ankmeiits.  the  se^'mental  arch  Avith  its  horizon- 
tal thrust  is  economical.  The  arch  thrust  resists  and 
counteracts  the  earth  pressure  on  the  sidewalls  from 
without. 

Hinged  Arches. 

A  i)ractice  tiiat  has  lon<r  l,t.,'n  followed  in  Europe, 
is  to  i)rovide  stone  (.r  metal  hinges  at  the  crown  and 
springs.  The  use  of  such  hinges  locates  definitely 
the  position  of  the  line  of  ])ressure  at  these  points, 
and  tliereliy  removes  om>  of  the  common  uncertain- 
ties i,(  masonry  bridges.  Hinges  are  particularly 
desirable  wliei-e  the  nature  of  the  soil  is  yielding  or 
uncertain.  Any  lateral  movenu-nt  of  the  abutments 
ciuises  the  andi  to  siidx  at  the  crown  when  the  centers 
iii-e  remove,!,  and  such  siiddng  produces  cracks  that 
are  unsightly  ami  [)ossibly  dangerous.  When  hinges 
are  used,  the  joints  are  filled  in  solid  with  cement 
niortar.  after  tii(>  .•enters  are  removed  and  the  arch 
ri!!ir  has  assumed  its  final  position.  For  additional 
loads,  the  entire  area  of  both  hinges  and  nu)rtar  fill- 
ing will  then  be  available  for  resistino  arch  thrusts. 


V 


p/.j/.v  co\CRi:rii  .ih'cii  nk'i/H;i:S. 
Position  of  Springs. 


U 


The  arch  spriii«rs  slioiild  he  located  as  iioar  1(» 
the  f(»iuulati(»ii  as  conditions  Avill  permit.  This  will 
reduce  the  overtiiriiiiijf  effect  on  the  pier  to  a  niiiii- 
nmni.  and  jiroduce  a  more  staltle  construction.  S(»me 
of  the  conditions  fjoverning  the  position  of  the 
springs  are  as  follows:  Over  streams  the  sprinj?  must 
be  sufficiently  hij;h  to  allow  ample  water  way.  and 
clearance  for  the  passajje  of  boats  or  drift:  over 
roads  or  hi«?hways  the  sprinjrs  must  be  sntlficiently 
hifrh  to  provide  proper  head  room  and  clearance  for 
the  [tassage  of  pedestrians  and  vehicles,  and  over 
railroads,  for  the  passajre  of  cars.  In  the  last  case 
there  must  be  a  cb-ar  head  room  of  at  least  21  feet 
at  a  distance  of  five  feet  from  the  face  of  ])iers. 
This  allows  clearance  for  the  lar<rest  box  cars  and 
additi(»nal  space  for  trainmen  on  the  roof. 

Abutment  Piers. 

For  ]()n<x  bridires  or  viaducts  with  a  series  of 
arches,  abutment  piers,  oi-  those  of  sufficient  thick- 
ness to  resist  the  pressure  of  a  sin<;le  arch,  should  be 
l)laced  at  frequent  intervals.  Where  the  spriujr  lin.' 
is  located  so  near  the  f<»undation.  that  piers  need  not 
be  excessively  thick,  it  may  ])e  dcj^irablc  to  have  all 
])iers  of  the  abutment  tyjie.  Then,  during?  the 
coui'se  of  construction,  the  spans  may  be  built  indc- 
]»endently  aiid  false  work  renu)ved  when  desired, 
without  reference  to  the  adjoining  spans,  or  after 
the  completion  of  the  bridge  if  oiu>  span  should  be 
destroyed   by  flood  or  othei"  cause,  the  other  spans 


12       (oxcRirn-:  liKiiKins  .ixn  cri.rnh-rs. 

would  still  ivmain  iiitii<-1.  IF  iill  piers  in  ati  arch 
\  ladiict  arc  of  the  ordinary  type,  to  support  vertical 
loads  only,  and  one  span  should  he  destroyed,  then 
Iho  nMn;)i?iin<r  spans  would  also  fall,  one  after  the 
other  in  succession,  hy  the  ovcrturninjr  of  successive 
piers. 

Height  of  Bridge. 

In  most  cases,  the  heijriit  of  Uw  hridj^c  or  level  of 
the  roadway  will  he  previously  deteniiined.  In  s(.nie 
cases,  h.  n-ev.'r,  tli.'  Iloor  jri;,.Ie  may  he  varied  nu)re 
or  less  hy  jrradiim"  the  approaches  to  suit  other  con- 
ditions. It  may  In-  that  money  spent  in  raisinjr  the 
iippi-oachcs  and  the  level  of  the  hrid^H'  floor,  will  he 
saved  many  limes  in  the  cost  of  the  masonry. 

Rise  and  Span. 

The  span  is  the  clear  distance  hetween  vertical 
faces  of  piei-s  or  ahntnuMits.  and  the  rise  is  the 
hciirht    (.f   crown    ahovc   s[)rin,irs.    measured    on    the 


hii 


•'  o!   pressure,     nd   not     <.n     the     arch     ititradc 


)S. 


Curves  joininL'  lh,>    arches  to  j)iers  are  not  part  of 
the  ct^'ective  rise. 

The  lenirlh  of  span  and  rise  of  andi  will  he  amoni,' 
the  first  c(.nsiderations.  In  many  cases,  the  natural 
•  •onditions  will  determine  cnie  or  hoth  of  these  di- 
ni.'nsi.u.s.  If  the  hrid.-e  is  short,  a  sin-l.'  span  mav 
he  sufficient.  If  it  spans  a  street  or  rapi.l  stroan'i. 
where  piers  are  impi'acticalde.  the  conditions  will 
'■''''"''■'■  ""'y  <>•>•'  ^Pit'i.  In  h.n-  viadu.-ts.  the 
dividin-  of  such  a  structure  into  spans  of  proper 
length  IS  an  imjH.rtant  matter.     The  economic  span 


V 


/7..//.V  coycRiiiii  .ih'cii  iik'inci-s. 


in 


the   total      li 


f 


l('ii<;tli  (Icpoiids  cliioHy  iipop.  the  total  liei»j'il  o 
slnjctiirc  above  foimdatioiis.  (iciicrally,  hi<ji:li  stnie- 
tiii-cs  i'('(|iiir('  loiijrer  spans,  juul  lower  strnctiires. 
shorter  spans.  For  steel  bridjres  with  vertieal  reac- 
tions, the  eeononiie  length  of  span  for  various 
iiei^'hts  is  Avell  known  or  may  easily  he  determined. 
l)ut  with  ai'ches  there  are  other  considerations.  The 
usual  i)ractice  is  as  follows: — IMace  the  sprin<;in}» 
lines  on  the  piers  down  to  the  lowest  point  jjossihle 
i-onsistc!;,  -\vitii  the  necessary  clearance,  and  tifter 
allowiniT  for  the  thickness  of  the  arch  rinjr  and  fill- 
intr  at  tlie  crown,  draw  in  spans,  the  len«rth  of  whi(di 
;ire  from  two  to  five  times  the  rise  of  the  arch.  ])ref- 
erence  beini;'  <iiven  to  sjtans  of  twice  the  i"ise  or  to 
semicirculai'  arches.  Certain  other  conditions,  how- 
ever, may  determine  the  leufjth  of  span.  P^)r  exam- 
ple, in  a  lonj?  viaduct  over  railroad  yards,  it  nmy 
he  desii-ed  to  span  a  certain  number  of  tracd^s  with 
each  andi.  or  to  have  as  few  piers  as  possible  t''  in- 
terfere with  additioiud  tracks  or  switches.  Tn  ihat 
ease,  the  len^rth  of  span  may  be  fixed  arbitrarily  re- 
u'ardless  of  the  rise  or  height  of  bridge. 

Tn  fixing  the  lengths  of  a  series  of  arch  spans,  the 
Romans  made  those  spans  nearest  to  the  center  of 
the  river,  loiiger  than  the  shore  spans.  The  plan  is 
still  in  general  use.  and  it  has  the  merit  of  causing 
the  span  at  a  distance  from  the  shore  observer,  to 
it]!ii(ar  at  least  as  long  as  the  nearer  ones.  "When 
a  uniform  s|)an  length  is  used,  the  eiTect  of  perspec- 
tivii  is  to  cause  those  spans  near  to  the  river  center 


14 


coxcui'.Ti-.  BRinci-s  .i\n  crf.rrRTS. 


I 


ihich  should   I) 


100.  to  appear 


which  shouul   l)t'  of  jjrrcator  iinpoi 
shorter  than  they  really  are. 

To  balanee  the  pier  thrust  from  unequal  s|>ana. 
the  shorter  one  may  have  a  smaller  rise  with  greater 
earth  tilling  and  eonsecpiently  greater  loads. 

Several  of  the  large  railroad  eompanies  have  re- 
cently adopted  standard  segmental  culvert  arches 
having  a  rise  of  one-fifth  the  span.  Tn  many  othei- 
bridges  this  proportion  is  exceeded,  especially 
where  natural  or  (»ther  conditions  govern.  General- 
ly speaking  it  will  be  found  cheaper  to  make  long 
spans  with  few  i)iers,  provided  sufficient  rise  is 
available. 

Crown  Thickness. 

Tn  the  preliminary  design  it  is  necessary  to  know 
approximately  the  retpiired  crown  thickness  or  dei)th 
of  keystone,  and  also  the  amount  of  earth  filling 
over  the  crown,  to  determine  the  remaining  distance 
from  crown  to  spring  or  the  available  height  for 
the  rise  of  arch.  The  crown  thickness  may  be  found 
approximately  by  reference  to  tables  of  existing 
arches,  (tr  from  some  reliable  empirical  formula. 
Trautwine's  formula  for  such  thi<d\nf>ss  is  as  fol- 
lows. ;i  development  of  the  formula  for  various 
sjians  aixl  rises  l)eing  given  in  the  Engineer's  Pocket 
Manuid 

Deplli  of  key  in  feet      ^  Radius+lialf  span  ^,o  f^ 

4       ■ 

The  above  is  for  the  jirst  class  cut  stone  work, 
either  circular  or  elliptical.  For  second  class  ma- 
sonry,   increase  the  results  from  the  above  formula 


PLAIX  COXCRRT/i  ARCH  PRIDCFS. 


1." 


by  ono-oi{?lith.  for  briek,  l)y  oiio  tbinl;  for  lar<r<' 
elliptical  arclu's  sonic  ciitriiiccrs  iiicrciisc  also  the 
;il)ovc  values  by  onc-tliii'd. 

Kaiikine's  nilc  for  crown  tbicl<ncss  is: — 


For  sinorlc  spans  \A'l  Radius 


For  several  spans  .  .17  Kadius 

Tt  bccomos  necessary  therefore  to  determine  the 
radius  at  the  crown.  This  can  be  done  jTraphically. 
The  crown  radius  for  an  ellipse  can  be  found  as 
described  later  and  sliown  in  Fi<rure  2.  Tt  is  com- 
mon practice  with  small  se«jmental  arches  to  maU'^ 
the  arch  ring  from  10  to  2.')  per  cent  thicker  than 
semicircular  ones. 

The  crown  thickness  nuiy  also  be  found  approxi- 
mately by  first  determinino;  the  approximate  crown 
thrust.  This  is  easily  computed  by  findinj;  the  cen- 
ter bending  moments  for  all  loads,  the  same  as  for  a 
beam,  and  then  dividing  by  the  rise,  or  the  approxi- 
mate crown  thrust  may  be  found  from  Xavier's 
rornuila,  Tr^/r,  where  T  is  the  crown  Ihrust,  p  the 
average  pressure  per  sipuire  unit  on  the  arch,  and  r 
Ihe  radius  of  arch  at  crown.  Tt  Avill  be  noted  that 
the  proper  value  for  the  crown  thrust  is  that  one 
which  produces  e(piili1)rium  about  the  point  of  rup- 
ture, and  not  about  the  springs. 

The  experience  of  the  writer  in  using  Trautwine's 
tables  of  sizes  and  quantities  for  masonry  arches  is 
lliat  Trautwine's  figures  are  about  one-third  larger 
than  the  best  practice  now  in  use  by  the  large  rail- 
road systems  for  tlie  design  of  concrete  arches. 


I 
I 


Mil 


16  (T).VC7v'/r/7:    HKIlHIliS    .IXD    Cn.rr.RTS. 

Thickness  of  Crown  Filling. 

An  assumed  (lei)th  for  tliis  filling  is  re<iuired  as 
noted   above,    in    order   to   determine    the   available 
heifjht  for  the  rise  of  the     areh.       For     highway 
bridges,  a  depth  of  filling  ineluding  the  pavement, 
of  from  one  to  two  feet  will   be  suffieient.  but   for 
railroad  struetures  a  greater  depth  is  neeessary  in 
order  to  form  a  eushion  for  the  ties  and  absorb  and 
ilistribute  the  shock   from  passing  trains.     For  this 
purjutse  a  depth  of  from  two  t(»  four  feet,  or  ordi- 
narily of  two  feet  below  the  ties  will  be  suffieient. 
To  secure  this  cushion  effect,  the  filling  in  some  re- 
een{    (-inerete    railroad    bridges   has   been    as    great 
as  five  feet. 

Spandrels. 

Bridge  spandrels  are  either  filbnl  solid  with  earth 
held  in   place  hy  side  retaining  walls,  or  the  fioor 
over  the  spandrels  is  supported  on  a  series  of  in- 
terior walls  and  arches,  which  may  or  may  no*  ap- 
pear on  the  exterior.    The  solid  earth  filling  h,  gen> 
erally  use,]  f,,,-  small  spans  and  fiat  arehes.    Hut  for 
large  arches  and   espeeially   semicircular  ones,   the 
op.'n  eonstruetion  will  be  cheaper.     In  eertain  eases 
of  eomparatively  flat  arehes,  even  where  it  would 
'"'  inor..  expensive  than  solid  filling,  the  open  .span- 
drel construction  nuiy  be  desirable  fur  the  purpos.^ 
of  reducing  the    load    on    the    foundations.     This 
was  the  ease  with  an  elliptical  arch  bridge  recently 


Pl.AIX  COXCRETE  ARCH  BRIDGES. 


17 


built  by  tlio  Illinois  Central  Railroad  Company  over 
!>i};  Muddy  Rivor.  containing  three  spans  of  140  feet 
caeh.  with  30  fret  rise.  It  was  found  that  the  open 
sparulrel  construetion  reduced  the  loading  on  the 
l)iles  by  about  six  tons  per  pii<'.  "Which  one  of 
llicsc  methods  to  use  in  any  particular  case,  can  be 
determined  l)y  juaUing  comparative  designs  and  es- 
timating the  costs.  In  many  cases,  however,  the 
clioice  caTi  l)e  made  by  inspection. 

liy  building  open  (diainbers  crosswise  of  the  bridge 
and  having  the  openings  appear  oi  the  spandrel 
faces,  a  design  is  produced  that  presents  a  lighter 
appearance  and  at  the  same  time  shows  plainly  the 
plan  of  cnnstruction.  When  a  heavier  and  more 
massive  appearance  is  desired,  theti  the  side  walls 
may  be  nsed  and  all  spandrel  openings  closed.  In 
large  arch's  ai)proaching  the  semicircular  form,  if 
open  spandrels  are  used  and  the  interior  spandrel 
walls  run  parallel  with  the  axis  of  the  bridge,  these 
walls  then  act  as  backing  and  produce  the  necessary 
conjugate  thrusts  on  the  haunches  below  the  points 
of  rupture.  The  jieed  of  i)r()viding  for  necessary 
con.jugate  thrusts  is  important  and  muse  not  be  over- 
looked. Cross  spandrel  walls  and  open  chambers  or 
arcades  may  be  used  above  the  point  of  rupture. 
l)ut  below  that  point  the  construction  must  be  solid. 
This  type  of  construction  is  well  illustrated  by  the; 
Connecticut  Avenue  bridge  at  Washington,  shown 
on  page  88. 


18 


COXCRlSTIi    BRinCI-.S   ASH   CII.II'.RTS. 


An  iiiij)r()\('(l  method  (tf  dcsij^iiin^  spaiidrcls  is  il- 
lustrated in  the  Piney  (Veek  Paraholie  Arcli  bridjje 
in  Washington.  The  (loor  slabs  are  carried  on  an 
interi(>r  system  of  beams  and  columns  supixjrted  on 
the  arch  iiii<r.  an<l  the  spandrels  are  enclosed  witli 
thin  curtain  walls.  A  desijrn  similar  to  this  for  a 
sejrniental  arch  was  prepared  by  Mr.  Thaeher  for 
llie  Hcllefield  bridfjre  in  Schenley  Park.  Pittsburtr 
'Phis  system  is  a  v<'i'y  economical  one  and  has  the 
advantajres  of  lea\  inj;  the  interior  construction  open 
at  all  times  foi-  inspection,  and  of  producinj?  a  less 
amount  of  load  in  the  spandrels  f(.r  the  arch  to 
larry.  T!ie  curtain  walls  are  also  thinner  than  re- 
tainin«r  \\alls  for  earth,  fillint;  and  cost  proportion- 
ately less,  and  the  pavement  nmy  be  laid  at  once 
without  waitinj;  for  the  Hllin«r  to  settle.  When  the 
pa\-ement  is  laid,  there  will  never  be  any  liability 
of  the  road  settlin<r.  as  often  does  occur  when  pave- 
ment is  laid  on  earth  fillinjr.  even  thou<rh  such,  fill- 
in;,'  be  well  rammed  and  permitted  to  settle  a  lon^' 
time  Itefore  laying  the  roadway. 

'Pile  use  of  the  open  spandrel  construction  with 
cither  ei-oss  Avails  or  columns  avoiils  any  uncirtainty 
in  i-efercuce  to  horizontal  <-on.jugate  pressure  from 
spandrel  tilling,  and  also  prevents  water  collecting 
and  soaking  into  the  arch  masonry.  When  it  is  de- 
sired to  secure  a  greater  diversity  in  design,  the  face 
walls  may  be  omitted  and  the  interior  arcade  or 
colonnade  construction  artistically  treated  for  the 


PLJix  coxCRi'.rr.  arch  PyRinci-.s. 


19 


purpose  of  prodiu'iiig  a  iiioro  pleasing  arehiteelural 
clTect.  In  eoinpariiig  the  relative  eosts  of  colon- 
nade and  areHtle  eonstruetion  for  spandrels,  en- 
closed column  construction  will  jjeiu  rally  be  found 
the  cheaper,  for  the  beams  and  columns  nuiy  be  left 
rough,  and  the  spandrel  curtain  wall  only  will  need 
a  finished  surface.  Cross  arcade  construction  has 
the  economy  of  snudl  dead  load,  but  all  open  span- 
drel walls  are  exposed  to  view  and  nniy  rerjuire  fin- 
ished surfaces  or  possibly  architectui  il  treatment. 
Open  chand)ers  may  be  enclosed  at  tlie  lop.  either 
by  means  of  arching  or  by  using  Hat  slabs  of 
stone  or  reinforced  concrete.  The  upper  surface  is 
then  waterproofed  by  ai)plying  a  layer  of  rich  mor- 
tar and  surfacing  with  neat  cement,  on  top  of  which 
is  poured  a  layer  of  tar  or  pit(di.  The  surface  may 
then  be  leveled  with  gravel  and  sand,  and  the  pave- 
ment laid. 

Another  reason  for  selecting  either  the  solid  or 
the  oi)en  spandrel  type  is  for  the  j)urpose  of  adjust- 
ing the  ijnposed  loads  on  the  arch  to  the  form 
selected.  This  may  be  necessary  to  secure  stability 
and  will  be  considered  later  under  the  head  of  load- 
ing. In  designing  the  side  spandrel  walls  to  retain 
earth  filling  the  usual  rules  for  retaining  walls  will 
apply.  Practice  is  to  make  the  thickness  of  such 
walls  at  the  base  40%  of  the  height.  They  should 
be  firmly  doweled  or  otherwise  secured  to  the  arch 
niasonrv. 


Si 


4 


20       C().\(h-i:iii  liKiiHii-.s  .\\n  cri.ii-.Ris. 

Various  Forms  and  How  to  Uraw  Them. 

Tlic  roriiis  iidnptcd  I'di'  tlic  iiitnidos  of  inasonry 
iin-li  Itr!(l<.'t's  i\n>  jri-iicrjilly  circnliir.  scj^incntal, 
t'lliplic.il.  or  iiiulti-ctMitcn'd.  TIm'sc  foui-  types  <'im 
Ih'  reduced  to  two.cireliliir  and  elliptical,  for  tliese;.'- 
iiieiilal  areli  is  iiier(dy  a  sejrment  of  a  circle,  and  the 
iindti-<'eiitere"(  areji  is  merely  an  approximate  ellipse, 
'i'lietwt  general  forms  are.  therefore,  the  circu- 
lar and  the  elliptical. 
Methods  of  drawing 
the  ellipse  and  the 
multi-eenteredcur\  e 
are  as  follows: 

Ellipse.  . 

Lit    A!)  and  CD 

»'  'he  semi-major 
fill  .spuii-minor  a\es 
of  an  ellips»>  at  rijrht 
anirles  to  each  other. 
Draw  circular  arcs 
with  radii  AD  and  ('D.  nsijectively.  From  points 
where  a  common  radius  intersects  the  two  circular 
arcs,  draw  vertical  and  horizontal  ordiuates.  The  in- 
tersection of  these  ordiKates<,nves  points  on  the  ellipse. 

Multi-Centered  Arch— Three  Centers. 

These  curves  are  sometimes  called  hasket-handlod 
arches.     The  uiethod   of  drawing  a   throe-centorod 


Fig.  1 


J 


PI..  \i\  c  7 )  \-(  h-r:  Ti-  .  / A'(  7/  liRii h:es. 


21 


^iin-li  is  as  follows: 
I.i't  AD  iiixl  (M) 
l»o  tlio  si'iiii-iiuijo. 
a  ii  II  (1      sciiii-miji  ir 
ax  OS.   respectively. 
^  of   a    true    ellipse. 
The    form    of    the 
true  ellipse  is  first 
<'  r  a  w  11      by    the 
method        <r  i  v  e  ii 
above.     This    is 
shown  ill  Fifrurc  2 
l>y    the    full    line. 
T  h  e  appro.xiinate 
form    is    then 
o  drawn  as  follows  : 
Assume  any  two  e.,iial  distanees  ("B  and  AK  less 
than  half  of  the  semi-minor  axis.  Joi,,  BE  and  biseet 
tlie  lin<>  P.K  at  F.     Throu<rh  F  draw  a  perpen.'    u- 
l;ii-  t(.  BK.  interseetinjr  th.e  line  (7)  at  ().     The  two 
I'"ints  O  and  K  will  be  eenters  of  two  eireular  ares 
which   will    form   an   approximate   ellipse.     By  first 
seleclin-  the  position  of  the  point  E  so  the  circular 
."v   describ(>d    fro,,,    E   as    center   will   conform    -.^ 
•losely  as  possible  with  the  true  ellipse,  satisfactory 
'•urves  will  easily  be  found.    The  full  line  on  Figure 
1'  shows  the  true  ellipse  and  the  dotted  line  the  ap- 
I'l'oxim.  te. 


22         COXCKETB   BRIDGES  AXD  Cri.rUNlS. 

Five-Centered  Arch. 

A  iiM'flHMl   fur  (IrjnviiijL'  a  fivf-cciilcn'd  iirch  is  as 
Tollows : — 

Til  order  \<>  dicfk  nn  tin-  v oik.  it   is  advisable  to 
llrst  draw  the  foriii  of  tlif  tnu*  ellipse  by  the  iiietliol 

•riven  above.  Tn 
Fii,'iire  :{  the  two 
curves  so  elosely 
eorrespond  that 
ojdy  one  oan  bi' 
shown.  On  th'' 
transverse  axis 
A()  draw  tile 
reetanjrle  ACICO. 
(Mliial  ill  lieiirhL 
to  the  senii-iiiinor 
axis  OC  of  tlie 
ellipse,  and  dr;:  w 
the  diajjoiial  A' '. 
From  G  draw  n 
line  OIID  per- 
l)endlcular  to  AC! 
and  intersect i II <r 
the     center     lir.e 


FiK.  :j 


CO  of  the  span  produced  at  D.  From  O  as  cen- 
ter, with  radius  OC,  draw  th(;  circular  ([uadrant 
as  shown.  Describe  the  stniicirclo  ARL  and 
imKluce  the  line  OC  to  it.s  inter.st-ctiou  with  tho 
semicircle  at  L.  From  O  as  center,  describe  tho 
arc  at  M  with  radius  equal  to  CL.  and  D  as  center  de- 


/V..//.V  c-().vcA'/  //:  .ih'cit  liRincns. 


23 


scriho  jirc  (f.M,  \\\\\\  DM  as  ni<l  is.  On  the  axis  AO 
liiy  off  AX  tM|ii)iI  In  Of,.  TIh'ii  fn.iii  II  ns  cciit.-r. 
with  nuliiis  IIX.  (Icscrihc  the  jirc  X(/.  ciittin};  M'l 
jit  a.  The  three  poii.ts  IT,  a  and  I),  with  corrfsixtiHJ- 
inp  OIK'S  ill  the  otlicr  «nui(lriiiit  nrc  the  tive  desired 
eeiiters  from  wliieh  to  draw  tlie  approximate  ellipse. 
This  method  of  drawing  a  five-eentered  arch  as  ap- 
proximate to  an  ellip.se  must  not  he  eonfouiided  with 
the  method  piven  later  for  drawin<r  a  hydrostatie 
arch.  The  eroM-n  radius  of  the  e]Ii{)se  will  l>e  less 
than  the  eorrespondinj;  radius  of  the  hydrostatie 
arch. 

Parabolic  Arch. 
The  paraltnja   is  not  fretpiontly  used   in  masonry 
hridjres.  hut  the  formula  for  drawintr  it  is  jjiven.     If 

is  as  follows  : — 
'  o       \  he  various  let- 

ters refer  to  di- 
meiisinns  shown  in 
the  a<'eompanyiii^ 
Fi''ure  4. 


y 


1  •«. » 


J-2  h 
rt2 


The  line  OK  is  divided  into  any  numher  <.f 
convenient  e(iual  i)arts,  whieli  are  luunhered  1.  'I,  W. 
etc.,  be<;iuuiuj,'  at  the  point  nearest  O.  Tlien  jo 
find  the  value  of  y,  for  the  various  ordinates  x.  the 
numbers  1,  2,  ,*{,  etc.,  may  be  inserted  in  the  above 
ecjuation  for  values  of  x,  and  the  total  number,  wliieli 
in  the  illustration  is  ^^,  will  be  inserted  for  the  value 


24 


COXCRETi:    HRinCES   AM)   (.77./ 7:' A' 7  .V. 


of  a.     Tilt'  upjHT  line   ill  Fiirurc  4  shows  tlir  corn's- 
poiitliii^  rorm  for  n  tnir  ellipse. 

A  \  ei'v  simple  jri-jipliiciil  luellHxl  of  (Irjnviii<r  the 
piirahol.i  is  t(»  hiy  ollf  on  llie  \-eftie;il  line  h'S  the 
sMiiie  iiuiiiher  of  eipuil  divisions  jis  di'invn  on  the 
liorizonliil  axis  OR.  and  fi'oiii  ()  draw  radialinjr  lines 
to  the  various  division  points  on  the  xcrtical  axis 
liS.  From  the  various  points  on  the  horizontal  lini' 
Oil  di'aw  vertical  lines  iiiterseetinjr  the  radiatiiiir 
lines  from  ().  The  |)oiiits  at  which  these  vertical 
lines  intersect  the  i-adiatin<r  lines  iwv  |)oints  on  the 
rctpiired   paraliolic  cnr\'e. 

Hydrostatic  and  Geostatic  Arches. 

In  selcctiii!.'  the  most  snitahle  form  for  the  iii- 
trados  of  an  ar(di.  the  followin<;'  i-onsideration  of 
the  ahove  two  forms  of  curves  will  he  serviceahle. 
The  hydrostatic  ai-ch  is  the  form  of  a  linear  arch 
under  varyinjr  pressures  wlii(di  are  always  normal 
to  the  line  of  arch.  This  condition  corresponds  t) 
that  of  an  andi  suhmer<r(;d  Ixdow  the  surface  of 
water.  As  the  dei>th  bi'low  the  surface  increases 
tlii'se  normal  pressures  increase  propoiM  ionately.  and 
as  the  external  pressures  are  always  normal  to  the 
snrfa<M'.  the  amount  of  pressure  in  the  arch  is  con- 
stant, and  is  ecpial  to  the  produce  of  the  external 
pressure  at  the  point  by  the  radius  of  curvatur.'. 
The  (Mjuation  is  T^-f^r.  and  is  known  as  Xavier's 
Prititiplc.  Since  the  essential  priiicipit!  of  the  hy- 
drostatic arch  is  that  lluid  pressure  is  normal  to 
the   surface,    the   thrusts   at   all    points   of  tlie  arch 


/7.J/.V  coxck'F.ri:  arch  hridgi-.s. 


i'iii<»  iirc.  tlicrol'iirc.  constiuit.  jind  ciniiiot  \  iiry  with- 
out the  iipplicatioii  of  >  '.'liuf  or  taiiffciitiiil  pres- 
sures. Since  T  is  cot  >;aiit.  /  \\\\]  -jiry  directly  as  /> 
Tliese  radii  may  \w  f  litid  for  va  yiuj;  de[)ths  belcnx 
water  level,  and  the  .  <  i  .•-^! -Midinj;  curve  plotted. 
It  will  be  noted  that  tht>  thrust  T  at  the  crown,  is 
equal  to  the  total  horizontal  pressure  on  the  e\- 
trados  of  half  the  arch. 

('•rdinarily.  liowevtM-.  arches  are  subjected  to  earth 
pressure  i-ather  than  water.  The  external  forces 
!.re,  therefoi-c.  no  lonjjer  normal  to  the  oxtrados 
of  the  arch,  but  ])ear  a  relation  thereto,  dependinjr 
on  the  nature  of  the  overlyini;  nuiterial.  Tn  the  case 
of  earth  or  <_M'avel  tillinpr.  haviiifr  an  an<rle  of  repose 
of  one  and  one-half  to  one.  it  is  known  that  the  hori- 
zontal pressure  exerted  atrainst  vertical  surfaces  is 
about  one-third  of  the  wei^'lit  of  the  material  above 

the  point  under  consideration.   Tho  formula  is  H  =  ^. 

The  linear  andi  suppoi-tin<r  a  filling  of  clean  dry 
sand  would  be  the  true  form  of  the  geostatie  arch. 
If  />  is  the  horizontal  intensity  of  force  in  the 
hydrostatic  arch,  and  p'  the  coiresponding  force  in 
the  geostatic  arch,  then  />r:r=r/''-  It  will  ])e  seen, 
therefore,  that  the  ureostatic  andi  bears  the  saiu" 
i-elation  to  \\\i'  liy<lrostatic  andi  as  the  ellipse  does 
to  the  circle.  A  linear  geostatic  arch  may.  there- 
fore, be  drawn  for  any  assumed  value  of  (",  sueh  as 
^.  which  ex|)erimeiits  show  to  be  about  the  right 
factor  for  earth  or  gravel  filling.  Tn  drawing  this 
linear  arch  all  the  vertical  co-ordinates  of  the  hydro- 


2<; 


(.oxcRF.TE  liRfncrs  .ixn  cn.rnRr.'^. 


stntic  iircli  ;u'('  rctiiiiicd.  iind  coiijnjrjitt'  prossni'os 
cliaiifri'tl  jici-onliiin'  to  the  foninilji  p^-Cp'.  Foi" 
;ii-clics  iukIci'  liciivy  l)iui]<s  ((f  cartli  the  geostatic 
anil  can  be  drawn  from  the  liydrostatio  areh.  Tl* 
tilt'  h('i<rlit  is  fixed,  the  form  of  em-ve  and  proper 
width  can  he  found  to  properly  witlistand  the  earth 
pressui'i".  For  lii'idjrt'.s.  these  principles  are  iiscful 
•■liictly  for  arches  under  hifrh  ciiihankments. 

In  his  hook  on  Civil  Kn^nneci'ing.  pajje  420.  Ran- 
kine  irivcs  the  following'  approxiiiiat.>  method  for 
drawiiifr  the  form  of  a  hydrostatic  curve  al)out  fivo 
centers  by  means  of  circular  arcs.     Tlie  two  radii  ;' 

~x  amir"  are  first  coniputt'd 
from  the  acc()nii)anyinLr 
formula.  Thi.s  fixes  two 
«)f  the  centers  and  the 
tliird  is  found  at  E  as 
shown.  The  e«[uati<»n.s 
for  radii  are  as  follows:  — 


0         T 


r^  - 


"  ii  +  ': 


a 


r  I   -f 

•»    \  !>■■ 

HP       y 

l)E      AF— BI) 


a 


b'—a'j 


^ 


PL.UX  iOXCRETF.  ARCH  BRIDGES. 


27 


f! 


Ill  Fitrurc  '>.  let  FB  bo  the  half  span  and  FA  the 
i-isc  of  tlio  proposed  arcli.  Make  A("=::=;-^,  and 
lJn=:i^;'',  the  radins  of  '•nrvatnro  at  the  crown  and 
sprinriii';  as  ealeulat.v.  from  tlie  ahove  fornmlae. 
Tlien  ('  -will  be  one  of  the  eenters  and  D  another. 
About  1),  witli  th(»  radins  I)E.  describe  a  circular 
;ir<'.  and  about  C",  -with  radins  CV.  describe  another 

circular  arc.  Let 
K  be  the  point  of 
intersection  o  f 
these  arcs.  Tin- 
points  D,  E  and  <J 
Mill  be  the  re- 
([uired  centers. 

]\rany  semi-ellip- 
tic arches  ap- 
l)roach  very  near- 
ly the  form  of  a 
hydrostatic  arch. 
A  comparison  be- 
twt't'U  Kaukine's  approximate  curve  and  the  true  one 
aie  shown  in  Figure  (!.  The  upper  or  outside  curvf* 
is  llie  api)roxiiiiate  eurve  as  given  by  Rankine.  The 
(•('liter  curve  is  the  true  hydrostatic  arch  plotted 
from  a  succession  of  radii,  and  the  inside  curve  is  a 
1  rue  ellipse. 

Selection  of  the  Most  Suitable  Form. 

Full  centered  arches,  either  circular  or  elliptical, 
produce  the  least  overturning  moment  on  the  i)iers. 
and  will   generally  require  less  pier  masonry  than 


l"lg.  G 


1 


i 


■ii#;et!..«-  « 


28 


cnxckniT.  BRincrs  axd  crr.rnRrs. 


s('<;mf'iit;il  ardics.  If  tlic  arch  thrusts  iijriiinst  iiat- 
iir;il  )-(K'k  sk('wt)iicks  or  al)iitiiu'iits.  the  niuouiit  of 
siicli  tlinist  is  then  a  iiiattcr  of  little  iinportaticc  as 
far  as  the  aljutiticnt  is  coticfnicd.  The  altafhiiicut 
of  sejrineiital  arches  to  piers  usually  re(|uires  tilted 
heds  to  l)riii<r  the  joints  at  ri^'ht  aiij,'les  to  the  liii(> 
of  jn-esstire.  This  is  a  condili.Mi  that  does  not  occur 
ill  full  (-entered  arches.  In  flat  ellipses  the  i)ier 
thrust  is  ^'■reater  than  with  seniicii-cular  ar(dies,  the 
position  of  thrust  api»roachin<>:  more  lu-arly  that  of 
a  seoiii(.nt;d  ai-(di.  It  has  already  been  shown  that. 
for  andi  culverts  carrying'  i  envy  earth  banks,  the 
sejrnieiital  form  of  arch  Avill  be  more  eflfectivo  and 
less  expensive.  It  produces  heavy  thrusts  on  the 
abutments,  which  thi-usts  counteract  the  inward 
pressure  of  tl;e  earth  on  the  side  i-etaininjr  walls. 
At  the  same  time  there  is  a  shorter  lenjjth  of  curved 
work  to  build  than  with  a  semi-circular  form.  The 
cost  of  seii'mental  culverts  has  been  shown  to  ])e 
only  about  (iO^;  of  tlie  cost  of  the  correspondintr 
semicircnlar  ones. 

After  drawin<r  a  trial  linear  arch  or  line  of  re- 
sistance for  any  particulai-  case,  the  form  of  this 
trial  curvi'  will  sufrjrest  the  most  suital)le  form  for 
the  intrados  of  the  structure.  For  a  brid<;e  with 
spandrel  filling'  jnid  londs  increasin«r  from  the  center 
to  the  spring's,  the  elliptical  form  or  a  correspond in.t? 
multi-centered  arch  will  probably  lie  lu-arest  to  the 
linear  aicli.  while  for  an  andi  with  open  spandrel.-! 
the  condition  of  loadinjr  will  be  more  nearly  uni- 
form, and  the  curve  will  be  flatter  at  the  haunches 


PL.UX  CO.VCRF.Tf:  ARCH  BRIDGES. 


29 


*    r 

If 


;ui(l  approncli  the  form  of  piirabola.  Tn  such  oasos 
llio  scs^iiiPiital  form  would  probably  bo  iisod  instead 
of  the  elliptical.  The  elliptical  form  requires  less 
filliiij?  in  the  haunches  than  the  segmental  arch,  and 
lias,  therefore.  l(>ss  weijLrht  to  carry.  At  the  same 
lime  it  <?ives  a  jrreater  amount  of  (dearanee  under- 
neath. \  semicircular  or  Roman  arcdi  with  a  lar<.'e 
rise  generally  re(iuires  the  smallest  piers,  and  in  a 
high  viaduct,  where  the  piers  are  an  important  part 
of  the  total  cost,  tliis  form  will  be  economical.  The 
exact  line  of  resistance  for  an  arch  luider  a  high 
eiidmnknuMit  is  the  geostatic  arcdi.  Tt  may.  how- 
ever, be  assumed  as  an  approximate  ellipse.  The 
form  of  the  intrados  under  earth  whose  angle  of 
re|)ose  is  :]0  degrees  Mill  then  be  determined  by  the 
iMluation  : — 

Vertical  axis  ■- 

H(n"izoiital  axis        A 
In  designing  culvert  arches  it  will  be  advisable  for 
the   engineer    to    consult    standard   plans   for  such 
structures.     ]\rany  considerations  will   appear  that 
might  not  at  first  occur  to  the  designer. 

External  Loads  and  Forces. 

Tt  has  already  been  shown  that  both  the  amount 
and  direction  of  the  external  forces  acting  on  a 
iiuisonry  arch  are  indefinite.  Tn  an  arch  supporting 
a  masonry  wall  it  is  usually  assumed  that  the  arch 
carrie.s  the  entire  weight  (»f  wall  above  it.  This 
is  on  the  side  of  safety,  but  is  certainly  not  correct. 
The   wall    will,   to   a   great    extent,   snnport   itself. 


.»■  ii  m 


m 


' " " .  m 


?,0 


coxch'iyrii  hkiih.hs  .\\n  cri.n-.Rrs. 


citluM-  iicliii<r  as  a  bfaiii  di-  ardi.  and  tlic  ]ir()liability 
is  that  till'  wcijrht  of  only  a  small  porlioii  of  llic 
wall  (lii-cctly  ahovc  llic  arch  is  iill  that  is  cari-ic  1 
directly  l»y  it.  Arches  under  hijrh  ('nd)anknionls 
certaiidx'  do  not  siippoi't  the  entire  wei^dit  of  earth 
ahove  thein.  The  earth  coi'hels  oi-  arcdies  itself,  as 
is  plainly  seen  in  the  case  of  a  tunnel,  where  oidy 
a  small  portion  above  the  crown  is  sni)])orted  by 
the  tuiuiel  center.  It  is  customary  to  consider  that 
andi  bridjres  \\\\\\  spandrel  (illinir  support  the  entire 
weiurht  of  such  filling-  on  the  ar(di  rin^r.  The  fact 
is.  however,  that  the  l)ackin«:  and  fill  either  arch 
thenisehcs.  to  some  extent.  fi"om  pier  to  pi(>r.  or  if 
the  hacking'  is  continuous  over  the  pier,  the  backinir 
itself  wiil  then  form  a  cantilever  and  carry  much  of 
the  s|)andi'ei  loads. 

The  Knjilish  enirineer.  llrunel.  uiany  years  n<ri> 
desiijiied  and  l)uilt  a  semi-arch  of  ])rick.  with  hoop 
iron  bond.  (iO  feet  in  len^Mli.  whicdi  supported  itself 
entirely  by  cantilever  action.  S;in(>e  the  introduc- 
tion of  reinforced  concrete  as  a  <lesirable  material 
tor  ai'ch  construction,  it  has  becon;(>  common  })i'ac- 
tice  to  build  cantilever  arms  oi-  bivud^ets  on.  the 
shore  ends  of  andi  spans.  showin<r  that  the  eanti- 
lever  principle  is  just  as  sure  to  come  into  action 
when  contiiuiity  over  the  j)iers  exists,  as  it  is  that 
the  andi  thi'ust  itself  is  in  operation.  A  jrood  illus- 
tration of  this  cantilever  construction  is  shoAvn  in  a 
bridjrc  recently  built  o\er  the  ^  rmilHon  Kiver  at 
\\  akeman.  Ohio,  and  di^seribed  in  Eufirineerinfr-Con- 
tracting.  February  1,  lOOf).  Somewhat  similar  eanti- 


PI.AIX  COXCRF.'I  i:  ARCH  BRIiHlI-.S. 


31 


lever  firms  were  used  t'cr  retaiiiiiifr  walls  iit  the  e\\i\^ 
of  Die  reinfnreed  eoiierete  iirell  hridfje  at  Topeka. 
Kansas. 

N'dt  only  is  llie  aiiiouiit  of  vertical  loading  from 
the  tilliii<;  unknown,  I -'t  the  horizontal  eon.jujjrate 
jii'essnre  on  the  masonry  haunches  is  also  indefinite. 
AVe  know  that  neai'ly  all  semicircular  arches,  or 
those  (jf  similar  form,  after  the  centers  a.re  removed, 
will  settle  at  the  crown  and  recede  laterally  at  the 
haunches.  The  effect  of  this  settlement  is  to  briny; 
i-onjujrate  pressure  on  the  l)ackin«rs.  and,  therefore. 
it  is  certain  that  pressure  exists  there,  but  the 
aiiiount  of  such  pressure  is  unknown.  Semicircular 
arches  re(|uire  backinj*  below  the  point  of  rupture 
to  produce  conjugate  pressure  eipial  in  amount  to 
the  crown  thrust.  This  must  be  secured,  either  from 
l)a(diing.  fill  tu-  spandrel  walls.  If  the  i)()int  of  rup- 
ture in  sefrinental  arches  is  at  or  near  the  skewbacd\, 
the  conjufrate  thrust  then  comes  from  the  abutment, 
and  little  or  no  backing  or  corresponding  walls  will 
be  ref|nired.  While  conjugate  pressures  are  neces- 
sary for  stability  below  the  point  of  rupture,  it  has 
lieeii  ilemonstrated  that  conjugate  tensions  are  nec- 
essary above  that  point,  and  to  secure  that  result, 
rods  have  been  used.  The  intensity  of  conjugate 
thrust  from  eai'th  lilling  with  an  angle  of  repose 
of  :W  degrees  is  oiu'-third  of  the  vertical.  It  is  good 
practice  to  cut  the  voussoir  stones  on  the  extrados 
of  the  arch  into  steps  with  horizontal  f.nd  vertical 
faces,  so  the  pressures  on  these  may  be  normal  to 
the  surfaces. 


32 


coxch'f-.Ti:  BRinr.rs  .ixn  cci.ri-.RT<!. 


Sclicnicr's  'riicorciii  ;issuiii('s  llijit  ,ill  external 
liiiidintr  jicts  verlieally.  'i'liis  is  an  error  uii  llu'  safe 
side  and  will  i-e(|nire  al»nliiients  sli<;hlly  heavier 
than  when  e()njn«rate  horizmital  forces  are  consid- 
ered. 

Tt  has  already  been  stated  that  elliptical  arches 
have  less  fill  or  material  ahove  th(.|ii.  and  conse- 
qnently  less  weijrht  to  carry,  than  either  se<ifnuMital 
or  parabolic  arches. 

Tn  the  case  of  arches  snpportinp:  earth  filling,  the 
form  of  such  tillinjr  will,  to  a  lar<r"  extent.  dete»'- 
mine  the  proportion  of  weijrht  that  bears  upon  the 
arch.  A  lon<r  brid<re  will  carry  the  entire  weijyht 
of  material  al)ove  it.  while  a  cnlvert  nnder  a  hij;li 
bank  will  carry  only  a  jxirtion  of  the  nnterial  above 
it.  Sewer  arches  exist  Avhich  would  be  unstable 
without  earth  jiressure.  showinjr  clearly  that  con- 
ju'jate  eai'th  pressure  does  exist. 

Mathematical  Theory  of  the  Arch. 

The  theoi-y  of  arches  is  very  complex  and  in- 
tricate. Analysts  have  <riven  much  thou«;ht  to  the 
matter  and  nuiny  voluiiu's  have  ])een  written,  when 
in  reality,  the  complete  determination  of  the  force 
polyj^on.  and  the  correspon(lin<r  line  of  resistance  in 
the  arch,  constitut.-  all  the  c;>lcidations  involved  in 
the  practical  (lesi«rii  of  a  masonry  arch.  All  methods 
of  comi)utation  are  approximate  only.  The  thick- 
ness of  arch  is  first  assumed  by  comjiarison  with 
tables  of  existing  arches  ,  ■  by  the  use  of  some  em- 
pirical fornuila.    Twines  of  resistance  are  then  drawn 


ri.UX  COXC'liTIi  ARCH  liRlDGIiS.  X] 

for  this  iin-h.  and  if  these  lines  (!<»  not  fall  within 
tho  mid  lie  tliird  of  the  arch  rinj?.  the  form  is 
elian<re<l  and  a  new  lin«>  of  resistanee  is  drawn  for 
the  revised  fonu.  The  ealenlations  resolve  them- 
selves into  a  series  of  trials.  Xo  effort  will  be  made 
here  even  to  review  the  many  theories  of  the  areli. 
For  siieh  investi<?ation  the  student  is  referred  to  the 
writiiifrs  of  mathematicians.  Their  eonelusions  oidy 
will  he  iriven  in  this  book.  The  theory  is  based 
upon  the  assumption  that  joints  will  i-esist  no  ten- 
sion. 

Stability  Requirements. 

The  re(|nirements  for  complete  stability  in  a  ma- 
sonry andi  are  three  in  number: 

(1)  There  shall  be  no  rotation  i>f  one  part  of  tin' 
arch  about  another. 

(2)  There  shall  be  no  sli(lin<r  of  one  surface  upon 
another. 

(•'{)  The  unit  pressure  shall  be  such  that  no  crush- 
ing of  the  arch  nuitei  id  shall  occur. 

To  insure  the  first  re(iuirement  it  is  necessary 
that  the  line  of  i-esistance  shall  lie  entirely  within 
the  arch  rin<r.  and  to  insure  further  that  the  pres- 
sure shall  be  distributed  across  the  entire  section 
of  the  arch,  and  no  tendency  to  openin<r  of  the  joints 
occur,  it  is  necessary  that  the  line  of  resistance  shall 
lie  within  the  middle  third  of  the  arch  rin<r.  To 
avoid  slidinjif  of  one  joint  ui)on  another,  all  joints, 
includinjr  those  in  tlie  arch  and  in  the  abutment, 
shall  make  an<rles  not  less  than  TO  deirrees  with  the 


i  I 


?A 


COSCRETE   BRIDGES   .IXP  Cll.VERTS. 


liiif  oi"  resistance.  The  frietinii  eoeffieient  for  ma- 
sonry joints  is  from  407r  to  :^{y/, .  To  avoid  crush- 
injr  of  the  areh  material,  the  eross-seetion  of  the  arch 
shall  1)e  sutlficient.so  that  the  intensity  of  pressure  at 
the  outer  edtre  shall  not  «'.\eee(l  a  certain  safe  work- 
injr  unit  With  these  three  re(|uirenients  fulfilled, 
the  stability  of  the  arch  is  assured.  If  a  line  oP 
resistance  cannot  be  drawn  within  the  middle  third 
of  the  areh  rin<r.  then  it  is  ru'cessary  to  change 
either: — 

(1)     The  thickness  of  the  arch  riujr. 

(2.)     The  form  of  the  arch,  or 

(.'})     The  distribution  of  the  loading;. 

Practii'c  in  tli  lesijjn  and  construction  of  con- 
crcfc  arches  \,ii.  ,  in  reference  to  the  absence  or 
presence  (»f  joints  in  the  areh  ring.  In  large  struc- 
tures, where  the  entire  c(»ncrete  cannot  be  placed 
from  one  mixing,  it  is  customary  and  sometimes 
necessary  to  provide  joints  in  the  arch  ring,  and  as 
an  additional  precaution  against  slidinj;  of  such 
.■•lints,  they  may  !)('  (btweled  or  d(»vetailed  together. 

Ultimate  Values. 

The  ultimate  crushing  values  of  the  common  arch 
materials  are  as  follows: 

(iranite    ....l.OOO  to  IS.OOO  ponnds   per  s(piare  inch 

Limestone    .4.000  "  10.000  "            "          "  <• 

Sandstone    .;}.()00  "  lO.OdO  ••            "          '•  << 

Concrete    ..2.000  "  4.000  "            ••          "  '« 

Brick    ;100  "  (iOO  "           •'         ■'  '< 


I'l.AlX  COXCRETH  ARCH  BRIDGES.  35 

Working  Units. 

Tli(>  workiiiir  unit  strcnfrtli  >f  flicsc  mnti-riiils  nt 
the  outer  ('(Ijrc  is  tnUcn  at  one-tenth  of  the  ultiniate. 
iuid  its  tlie  inaxinmni  pressure  at  the  outer  edpe 
when  pressure  at  tlie  inner  edfre  is  zero,  is  twice  the 
mean  or  averajre  pressur*".  this  correspomls  to  usin^' 
a  mean  unit  i)ressure  of  only  one-twentieth  of  tlie 
ultimate.  The  necessity  for  this  hijrh  factor  will  be 
seen  from  the  following:  considerations.  Experi- 
mental (lata  on  the  strenjrth  of  masonry  in  bulk  is 
comparatively  small.  .Most  experiments  have  been 
made  on  sample  pieces  of  the  material  held  properly 
in  position  with  pressures  applied  normal  to  sur- 
faces. Also  the  crushing'  streu*rth  of  masonry  in 
bulk  is  nuich  less  than  that  of  the  separate  material 
of  which  it  is  composed.  Ix-cause  of  the  presence  of 
mortar  joints.  On  the  other  hanjl.  experiments  were 
made  on  sami>le  cubes  of  material,  while  in  the 
arch  the  mjileri.il  is  used  in  btr<;e  mass,  ami  is. 
therefore,  stron'.'er  than  cubes.  Errors  in  workman- 
ship and  in  fittinjr  of  joints  may  cause  excessive 
|)ressure  to  occur  on  sonu'  i)arts  of  joints,  and  little 
oi'  none  at  all  on  other  i>arts.  The  entire  system  of 
external  loads  is,  Ihcrefore,  uncertain.  Working? 
luiits  may  safely  be  taken  as  follows: 

(•ranite .')00  to  ]..")00  ])ounds  per  square  inch 

Limestone     ..  .300  "    1.000 

Sandstoiu" 200  *'       SOO 

Concrete 200  '•      .lOO       "  "         "         " 

T.rick 80  '^       100       "  "         " 


I 


:!fi 


LoWRi.ii-  iii<iiH,i:S  .ixn  cri.i  i.h'is. 


A  iiiiixiiiiiiin  pri'ssiifc  of  |(Ht  |iiiiiiiils  per  si|ujir<' 
iiH'li  is  irund  inMclicc  for  ('(HHTt'lr  jin*li  rinjrs.  and 
is  suitjihlr  for  a  iiiixtui'c  of  1-2-4  •\V(>11  and  carefully 
laid. 

Tlic  alxtvc  pressures  refer  to  the  niaxiinuin  pres- 
sure at  llie  (Mitef  edjrc  and  not  to  the  mean  or  avor- 
ajre  pressnre.  whieh  wonld  he  only  one-half  of  the 
ahove.  These  niiits  will  ffive  a  faetor  of  safety  of 
ten  in  eonipi'ession.  The  re(|nirenient  that  the  line 
of  resistanee  shall  fall  within  the  middle  third  of 
the  joint  prodnees  a  factor  of  safety  ajrainst  rota- 
ti(»n  of  three,  and  the  re<piiremen1  that  the  an<rle 
hetAVeen  the  face  of  joints  and  tlx'  line  of  resistanee 

he   not    less   than    70   de<ri s   prodnees   a    fa<'t<M'   of 

safety  a<rainst  slidin<r  of  from   one  and  one-half  to 


two. 


Determination  of  Line  of  Resistance. 


<  )r(linarily.  the  consideration  of  two  cases  <<['  load- 
ing' will  he  sut!icienl.  (1  i  A  nniform  dead  and  livi' 
load  ovei-  the  entire  strnctnrr.  and  (2^  the  entii-' 
•  1'  load  with  a  maxiimnii  li\<'  load  over  one-half 
of  the  span  oidy.  The  ahsolute  maxiiiium  stresses 
fr<»m  i)artial  loadin<r  may  he  ohtained  when  the  live 
load  is  applied  to  somewhat  less  than  one-half  th(> 
span,  as  .4  to  .4."i  of  the  lenjrtli.  l)nt  for  practical 
pnrposes;  it  is  snfticiently  a<'<Mirate  to  consider  half 
the  span  loaded.  In  certain  cases  it  may  he  neces- 
sary to  consider  the  maximiun  dead  load  with  a 
siiifxle      concentrated     liv(>     load     at     the     center. 


f'L.iix  coMki.ii:    ih'iii  nh'iiH.i  s  ?,i 

V\Ui\  first  tlic  line  uf  i-csislaticf  Ww  lln'  ninNiimiiM 
(Icjid  nud  Ii\('  Idjids  oxer  tin-  I'litirc  stnicliirc  An 
!ij)proxiniato  tliickncss  will  linvc  Ixmmi  assumed  for 
the  iircli  rin?  nt  the  confer,  also  flic  tlepfli  of  flic 
ciirth  filliiitr  above  as  previously  described,  and  an 
approximate  f<irm  <>f  arcli  will  bave  been  selected. 
11"  fbe  l)ridjre  lias  spnndrel  tilling  flie  first  operation 
M  ill  be  to  divide  fbe  loaded  ai-en  above  fbe  intrados 
into  a  lunnber  of  vertical  strips,  to  compute  fb" 
weijrbt  of  material  in  ea<di  of  tbese  strips  and  tbe 
live  load  (>•  tbem.  i.:  order  to  simplify  :  '  -iilafions. 
a  portion  nf  fbe  bridjre  one  f(tot  in  leti  '■>  ;  t  rijrbt 
ansrles  to  fbe  paper  will  !»(>  considered.  Eacb  re- 
iiiainitifr  p<  rfion  will  be  a  dui)licate  of  fbis.  Tt  may 
be  necessary  to  draw  a  separate  line  of  resistance 
under  tbe  side  spandrel  walls,  because  fbe  weifibt 
of  wall  uuisonry  is  {rreater  fban  eartb  fill.  The 
amount  of  eon.ju<;ate  pre  sure  of  fbe  backintj  on  the 
bauncbes  is  then  considered.  For  prravel  and  eartb 
fbe  intensity  of  this  pressure  ))er  sfpuire  foot  or 
otiier  unit  may  be  taken  at  one-tbird  of  tbe  weifjht 
of  fillinjr  and  live  load  above  tbe  extrados  at  fbe 
strip  under  consideraf ion  Then  the  prodnct  of 
this  horizontal  intensify  and  fbe  area  of  the  vertical 
projection  of  that  i)orfioii  of  the  extrados  nnder  tbe 
strip  will  jrive  fbe  amount  of  the  conjnjjrafe  fbrusf. 
This  will  be  repeated  for  all  other  strips  and  a 
complete  set  of  loadings  found,  which  slioubl  all  be 
written  in  their  respeetise  places. 


Ill 


if 


MM 


I'! 


PI.AIX  COXCRr.TIi  .IRC! I  BRinCES. 


no 


I'rncood  next  to  construct  a  forc(>  jiolygoii 
by  drjnvijifjc  tlie  varioiis  loadiiifrs  to  a  convenient 
scale.  As  arches  are  frenerally  synniiotrical  about 
tbe  center  and  liorizontal  at  that  |)oint.  the  crown 
thrust  for  uniforni  loadin<rs  will  likewise  be  hori- 
zontai.  The  pole  in  Ihe  force  j)oly«;on  will,  there- 
fore, be  on  the  same  hoi'izontal  line  with  the  upper 
end  of  the  first  load  line  a1  A.  The  amount  of  this 
crown  thrust  is  unknown,  and  the  pole  distance  can, 
therefore,  be  oidy  assumed  for  the  present.  Tako 
any  pole,  as  that  shown  at  V  on  Figure  7,  and  draw 
the  corresponding  force  polygon.  Draw  also  the 
corresponding  line  of  resistance  or  funicular  poly- 
gon in  the  arch  ring,  starting  from  any  point  within 
the  middle  third  at  the  crown.  The  resulting  funic- 
ular polygon  is  that  shown  at  ay'.  Tt  is  evident 
that  the  pole  distance  assumed  was  uo\  the  correct 
amount  of  the  crown  thrust,  for  the  line  of  resistance 
or  polygon  falls  entirely  outside  of  the  arch  ring. 
Project  the  last  line  of  the  funicular  p<»lygon  till  it 
intersects  the  line  of  ci'own  ]iressure  produced  at 
the  point  ir.  This  gives  the  jiosition  of  the  resultant 
of  the  assumed  loads,  and  its  direction  will  be  pai'- 
allel  to  the  line  \\\  in  the  force  jiolygon.  The  posi- 
tion of  this  resultant  is  constant,  regardless  of  the 
forc<>  polygon.  Tlierefore.  the  corresponding  line 
of  any  other  funi<'ular  polyiron  produced,  such  as 
that  through  y.  will  likewise  intersect  at  the  same 
point.     Therefore,  through  y  draw  such  a  line,  and 


! 


40 


COXCRllTE   BRIDGES   AXD   CVU'ERTS. 


1\ 


from  B  in  the  force  i)oly«.'on  draw  liP.  iiitersoctins: 
the  horizontal  throu*;li  A  at  P.  Tlie  distance  Al"* 
measured  to  tlie  same  scale  as  the  load  line  will 
represent  tlie  true  amount  of  the  crown  thrust.  The 
(tlher  lines  radiatinj;  from  V  to  the  various  points 
on  the  load  Ime  will  tndy  represent  the  amount  of 
thrust  at  the  various  points  in  the  arch. 

A  check  on  the  crown  thrust  may  be  made  by 
findinir  the  bendin«r  moment  at  the  center  for  all  the 
loads  in  the  same  way  as  for  a  beam,  and  dividing 
this  moment  by  the  rise  of  the  areh.  It  will  be 
remembered,  however,  that  the  rise  is  not  neces- 
sarily the  distance  from  spring  to  crown,  for  in 
flat  ai-ches.  arid  es])crially  in  elliptical  forms,  the 
line  of  rt'sistance  does  not  fall  as  low  as  the  springs. 
The  correct  rise  of  an  arch  is  the  rise  of  the  line  of 
resistance  and  not  the  rise  of  intrados  from  spring 
to  crown. 

It  Avill  be  seen  by  iiisp<'ctioii  that  a  positiou  of 
the  ])oiiit  y  was  selected  so  the  line  of  pressure 
would  not  pass  outside  of  the  middle  third  of  the 
ai'i'h.  It  approaches  iicafcst  to  the  limit  under  the 
strip  (/.  The  point  opposite  to  this  limiting  position 
is  caUed  the  point  of  rupture,  and  is  the  point 
at  which  the  arch  fii'st  tends  to  open  at  the  cx- 
trados.  If  the  line  of  resistance  from  the  assumed 
])ni!it  V  h'ld  fntlen  oi/si(l(>  tlie  middle  third  of  ihe 
arch  ring  at  (/.  a  new  point  would  then  have  been 
assumed  so  as  to  bring  tlie  line   of  resistance  en- 


PL.^IN  C0\' CRETE  ARC  1 1  BRIDGES. 


41 


tiroly  witliin  the  iniddk'  third  at  the  point  of  rup- 
ture. As  this  point  v  would  ap{)roa('li  vory  close 
to  the  niiddlo  third  for  an  arch  of  uniform  thick- 
n''ss  from  crown  to  sprinjr.  the  rinj;  is  thickened 
at  tlie  hauncdi  to  keep  the  line  of  resistance  well 
within  the  middle  third.  The  line  ay,  which  falls 
entii'cly  within  this  limitinjr  space,  is,  therefore,  a 
true  line  of  resistance  for  the  maxinunii  assumed 
dead  and  live  loads.  It  Avas  necessary  to  determine 
the  crown  thrust  or  pole  distance  liy  trial,  because 
there  are  four  unknowu  (piantities,  the  two  vertical 
and  the  two  horizontal  reactions  of  the  a..'h,  and 
to  determiiu'  these  there  are  only  the  three  equa- 
tions of  eciuilihrimn,  .^'ar- 0,  ^y—O,  2m~  0.  The 
line  BP  applied  at  the  point  y.  represents  truly  in 
both  direction  and  amount,  the  thrust  of  the  arch 
on  the  abutment.  This  may  be  resolved  into  ver- 
tical and  horizontal  comj^onents  as  shown. 

Xumerons  injjenious  methods  aave  ])een  adopted 
for  simplifyiiif?  the  computations.  For  instance. 
"  Avriters  prefer  to  construct  what  they  call  a 
I  .ced  load  contour.  This  consists  in  first  finding 
actual  loads  of  arch  rinj?.  fill,  live  loads,  etc., 
•"or  cacli  vertical  strip,  and  reducing;  the  height 
above  the  extrados  to  a  correspondinp:  height,  pro- 
vided tlie  load  was  caused  entirely  from  stone  or 
matei'ial  of  the  same  nature  as  tlie  arch  ring.  Plot- 
ting these  various  heights  to  scale  abo'c  the  in- 
trados,   and   coiuieeting   the   points   so   found,   pro- 


42 


COXCRETE   BRIDGES   A\'D   CVLVERTS. 


(lucos  n  liiH>  which  is  cnllcd  tli<'  rodiiccd  load  eon- 
four.  TJicn  l>y  iiinkiiig  the  divisions  two  feet  in 
width,  and  scaliiij;  the  leiijrth  of  the  two  sides  of 
each  strip,  the  sum  of  the  len<rths  s<'aled  will  repre- 
sent the  area  of  the  enclosed  strip.  Sometimes  the 
areas  are  i)lot1ed  on  the  load  line  of  the  force 
polytron  instead  of  the  weights. 

Practic(>  varies  somewhat  in  reference  to  the 
selectin<r  of  tlie  jiroper  jxtint  in  the  middle  third 
of  the  arch  crown  from  which  to  draw  the  line  of 
resistance.  ^Vhen  a  h'njre  occurs  at  the  crown  there 
is  'hen  no  uncertaint v  as  to  the  correct  position  of 
the  line  (tf  thrust.  Some  designers  consider  that 
the  position  of  the  line  of  resistance  is  such  as  to 
make  the  crown  thrust  a  minimum  without  causing 
tension  on  any  i>art  of  tiie  section.  To  satisfy  these 
conditions,  the  line  woidtl  pass  through  the  upper 
extremity  of  tlie  middle  third  at  the  crown,  and  at 
the  si»rin,<rs  or  at  the  points  of  rupture,  the  line  of 
resistance  would  pass  through  the  inner  extremity 
of  the  middle  third.  Professor  Church  says  that 
the  trne  line  of  resist.nnee  is  that  one  corresponding 
most  neai'ly  with  the  center  line  of  the  arch. 

Tin    intensity  of  the   unit   pressure  on   a  surface 
may  he  I'ound  from  the  following  f ornuila : — 
p  ^  W       OWd 

"^  L  L-' 

\vli(>re  p  is  the  niaximnm  unit  pressure  at  any  part 
of  a  joint.  W  the  total  pressure,  d  the  distance  of 


PLAry  COXCRRTP.  ARCH  nRIDGF.S. 


n 


p  = 


the  ocjitcr  of  pressure  from  the  center  of  the  areli 
ring,  juxl  L  the  depth  of  the  jirch  ring.  The  formula 
is  general  for  all  positions  of  d,  provided  the  joints 
can  resist  .ension.  Tf  they  cannot  resist  tension, 
the  formula  is  still  general  for  the  values  of  d  up  to 
one-sixth  of  L.  Tf  d  exceeds  this  amount  the  max- 
iiinim  pressure  is  tlien  given  l)y  the  formula: — 

.'{  (one  half  L  -  rf) 
The  amount  of  crown  thrust  or  i>ole  distance  may 
he  found  analytically  by  taking  moments  succes- 
si\('ly  around  the  various  load  ])oints  in  the  arch. 
The  crown  thrust  will  be  found  a  maximum  wlien 
monu'nts  are  laivcn  about  the  load  point  opposite 
to  the  point  of  ru]itnre.  This  is  an  analytical 
method  of  locating  the  point  of  rupture. 

If  the  arch  had  hinges  at  the  crown  aTid  springs, 
as  are  commonly  built  in  Europe,  the  crown  thrust 
eould  then  ])e  detinitely  figured.  The  presence  of 
such  hinges  greatly  facilitates  the  computations  for 
partial  loading,  for  then.  Tiot  only  the  amount  of 
the  crown  thrust,  ])ut  also  its  direction,  are  un- 
known.   It  is  no  longer  a  horizontal  thrust. 

The  above  method  of  drawing  a  line  of  resistance 
for  uniform  loads  applied  to  a  pair  of  scgmentul 
arches  is  illustrated  also  m  the  left  hand  arch  of 
Figure  10. 


44 


coxch'r.rr.  HKincr.s  .\xn  cuij-rr-'s. 


A  iii<»(li(icati(.ii  c.f  llio  abovo  nicthod  of  dplorrr  in 
in«;  the  crown  thrust  and  drawing  the  lino  of  ro- 
sistanco  is  shown  in  Figure  8.  The  space  above  the 
arch  ring  is  divided  as  l)efore  into  ten  equal  divi- 
sions and  the  t<.tal  load  on  ca(di  calculated  and  indi- 
cated in  the  proper  places.  Beginning  at  the  point 
IJ.  which  is  the  upper  extremity  of  the  middle  third 
at  tlic  crown,  the  loads  for  half  the  arch  are  meas- 


ly:: 


FlK.  8 


ured  off  to  scale  on  a  vertical  load  line  \\c.  From 
R  and  c  di-aw  lines  at  4.-)  degrees  with  the  vertical 
intersecting  at  0.  and  from  O  draw  lines  to  tiic 
points  a,  b,  c  and  d.  Construct  a  polygon  with  sides 
i>'n-allcl  to  the  lines  Oa,  0^;.  Or,  O,/  and  Oc  and  ex- 
tend the  two  extreme  lines  of  this  polvgon  to  their 
intersection  at  D.    Through  D  draw  the  vertical  CE 


PL  A IX  coxck'iirr.  arch  bridges.  43 

intorseetins  tli,.  horizontal  line  R  at  C.    The  line  CK 
marks  the  center  of  jfravity  of  the  loads  on  the  five 
areh  divisions.     Thron-h   C  draw   the   line   CS  so 
that  the  line   of  resistance,   when    drawn,   will    lie 
within  the  middle   third   of  the  areh    rin-      After 
drawinprthe  line  of  r.'sistanee,  if  it  should  be  found 
that  any  part  of  it  falls  without  the  middle  third 
a  new  position  must  then  be  assumed  for  the  point 
S.     Throu-h  c  draw  the  horizontal  line  EF,  inter- 
seetin-  f'S  prolon-ed  at  F.    The  line  FC  will'  repre- 
sent truly  to  seale  the  amount  of  the  crown  thrust 
From  R  lay  off  <,„  a  horizontal  line  through  R    the 
distance  RI>,  oc.ual  to  FE,  and  join  P  with  the  points 
a,  h,  c,  d  and  c.    From  R  draw  the  line  of  resistance 
with  sides  parallel  to  the  lines  Pa,  Vb,  etc.     If  any 
part  of  this  line  of  resistance  falls  outside  of  the 
"•'ddle  thinl  of  the  arch  ring,  a  new  position  must 
then  be  assume<l  for  the  point  S,  and  another  line 
of  resistance  drawn,  falling  entirely  within  the  mid- 
dle third.      If   no   such   line    of   resistance    can    bo 
drawn,  then  cither  the  form  of  the  arch  or  its  thick- 
ness must  be  changed  until  a  line  of  resistance  can 
»'•'  drawn  lying  entirely  within  the  middle  third. 


I* 


\ 


i 


Line  of  Resistance— Partial  Loading. 

Consider  next  the  case   of  a  maximum  live  load 
"v<>r    half    the    span,    acting    in    conjunction    with 


.1^  i' 


PI..HX  COXCRETF.  ARCH  BRWCP.S. 


47 


1 


the  inaxiinum  dead  load.  Tioth  lialvcs  of  tho  arch 
iimst  then  Ik-  considered.  As  before,  the  portion 
of  the  bridge  above  the  intrados  is  divided  inti» 
vertical  strips,  and  tlie  vertical  and  conjugate  load- 
ing's written  down  in  their  respective  places.  A 
load  line,  AHC,  is  drawn,  and  any  trial  pole,  P', 
assumed.  With  this  position  of  pole,  the  funicular 
polygron  shown  in  dotted  lines  is  drawn.  By  usinj,' 
a  little  care,  the  point  .r  may  be  selected,  so  the 
curve  on  the  left  will  fall  within  the  middle  th.rd. 
or  tangent  to  it.  It  will  be  .seen  that  this  line  of 
resistance  shown  dotted,  falls  outside  of  the  middle 
third  in  two  places  and  intersects  the  outer  vertical 
through  c'  at  y.  This  cu*  ve  cuts  the  center  line 
of  arch  at  /'.  See  if  it  is  possible  io  draw  another 
line  of  resistance,  so  that  it  will  cut  the  center  of 
the  span  at  the  point  /  and  pa.ss  through  the  point  \. 
From  I"  draw  a  line  i)arallel  to  /'  y'  intersecting 
AB  at  D,  and  from  D  draw  another  line  DP  parallel 
to  ty.  The  new  pole  will  lie  on  the  line  DP.  Also 
through  P'  draw  a  line  parallel  to  xy'  intersecting 
the  load  line  in  Q,  and  from  Q  draw  another  line  QP 
I)arallel  to  .ry.  intersecting  the  line  DP  at  P.  The 
point  will  be  the  correct  jiosition  of  the  jiole,  in 
order  to  have  the  line  of  resistance  pass  through 
the  three  points,  .r.  /  and  y.  The  distance  II  in  lh<* 
force  polygon  may  be  verified  analytically  as  fol- 
lows : — 


u 

Cij 

:i 

•j5 

g 

>» 

L. 

^ 

it 

"J 

3 

•^ 

u 

L« 

•J 

n 

0 

X 

'^ 

- 

t 

2 

c^ 

m-: 

w 

^ 

:5 

*" 

•^ 

^ 

r3 

!>•, 

ri 

7* 

n 

J2 

.5 

w 

:: 

c 

3 

3 

"( 

w 

>, 

c 

s 

c 

i 

-/. 

I.*: 

a 

~ 

?■ 

rr 

-3 

.2 

/. 

fl 

■r 

>, 

ii 

-^ 

•^ 

V 

— 

M 

•^ 

■r. 

~ 

^ 

r3 

T 

■^ 

*> 

w 

u 

h 

^  — 

«*-« 

*i 

i: 

iJ 

<«-) 

■^ 

'•I 

•J 
1 

> 

0 

■i 

E 

4>^ 

3 
2 

5 

£ 

K 

tr 

i 

r. 

•3 

*-> 

•^ 

V 

0 

'< 

h 

^ 

•-C 

4>J 

•^ 

\j 

s 

"'j 

^        c^ 

'7 

*/: 

3 

:i 

w 

'— 

•J 

S      c 

,a 

w 

0 

•S 

S,  5 


5^  i  2 


2  H 


2  '^ 

o   a 

■A     ^     «3 


I  ^  3  «  1^  I  ^' 


■A 

^ 

? 

^ 

Ci 

s 

7i 

>■* 

1- 

•<-> 

n 

2 

V-> 

4-1 

:; 

^ 

.«.j 

•S 

.^* 

^ 

<J 

■^ 

>i 

*^ 

J^ 

;!^ 

^ 

>•* 

3 

S 

3 

^ 

<<-i 

0 

:; 

u 

^ 

i3 

C 

S 

'^ 

ii 

-. 

c 

3 

rs 

w 

w 

^ 

^ 

- 

rt 

p 

t£ 

ri 

^ 

<«H 

't-j 

X 

*sZ 

H 

J5 

73 

-1 

1 

- 

'^ 

— H 

^ 

^ 

V 

4^ 

> 

h-i 

^ 

•J 

•4^ 

s 

r 

0 

V 

cS 

:5 

•w 

4^ 

fr 


■ 

1 


iKl^ 


PLAIX  COXCRETE  ARCH  BRIDGES.  49 

H'X/'A:'  =  HX/A-. 
From  this  oriviation  th(>  valuo  of  II  may  ho  found. 
Mii'I  the  point  I'  will  lie  on  the  line  (^I*  at  a  distanci' 
II  from  the  load  lino.  Tho  lino  (»f  rcsistanct'  xt\  is 
tan<ront  to  tho  lino  of  middle  third  in  tho  strij)  </. 
Tho  point  whoro  linos  hooomo  tanjront  niljjht  havo 
boon  takon  as  tho  rocpiirod  point  throufrh  whioh. 
with  .r  and  /.  it  was  dosirod  to  pass  a  lino  of  ro- 
sistanoo.  Tho  oorrospondinsjr  lino  would  havo  boon 
found  in  a  niannor  similar  to  that  dosorihed.  It 
will  1)0  soon  that  tho  lino  .i7v  lios  ontiroly  within 
the  middle  third  of  tho  aroh.  and  tho  aroh  as  drawn 
is,  therefore,  stable.  If  it  had  boon  found  impossible 
to  draw  a  line  of  resistance  within  the  limits  of  the 
middle  third,  it  would  havo  been  necessary  to 
chan^'e  either  (1)  the  form  of  tho  arch;  (2)  tho 
thickness  of  the  arch;  or  (:})  the  distribution  of  the 
arch  loadinj?.  A  similar  method  applied  to  soj?- 
mental  arches  is  shown  in  Fiijuro  10.  In  this 
case  the  bridfjo  Avas  desi«rned  to  carry  a  double 
line  of  railroad,  with  tracks  ],'>  feet  apart  on 
centers.  It  was  assumed  that  the  ties  and  earth  fill- 
in£j  distribute  the  weight  of  each  track  aiul  tho  live 
load  thereon  evenly  over  one-half  tho  Avidth  of  the 
liridge.  This  assumption  iiuiy  not  be  true,  but  it 
is  as  reasonable  an  y\  h  ixinuition  as  can  be  made. 
The  live  load  was  assumed  e(pial  to  Cooper's  stand- 
ard E  50,  and  for  3'-foot  spans  is  equivalent  to  a 
uniform  live  load  of  10.000  pounds  per  lineal  foot, 
which  was  considered  evenly  distributed  over  a 
width  of  15  foot,  fimounting  to  HfiT  pounds  per  lineal 


1 


|^_  -^Pliq 


.-,0 


cowRf-ri:  ni.i!>(,i:s  .ixp  cniiii^is. 


! 


font  in  widll  n\-  1,  ii1u.'.  For  i>nrti;il  loa.linjr.  the 
•  •"iniviilriit  iiriifuiiii  li\.'  load  on  linlf  tin'  span  was 
assniiicd  at   ll.r»(lo  jM.nnds  [xt  foot  of  track. 

I'oint  oi  Aupture. 

Tlic  point  of  r  i!  ,:■!•  .^  tliat  point  of  tlio  ai  1) 
I'liij:  at  tlir  hantniM  -  '••;<•?•  tli.'  joints  tend  to  oppii 
al   the  cxtrados.    m    vhi"f  t  i.'  Imc  of  rcsistanco  li<-s 

'•loscst    to    the    idiht     ..,)m-.    ,,;    fl    '    ardi.       I5y    s. • 

writers  this  poiiu  ;.,  coi, ,.  [fri'd  fhc  real  sprin«,'i!  j? 
point  of  tin-  arcli.  ;i,id  an;  i  rt  ..f  the  an-h  Ix-l.-w 
IIk'  point  of  niptnrc  iv  cons  h-rci  as  part  of  •  he 
pier  ..r  al)ntni.'iit.  [is  position  -an  l»(>st  ho  dotcr- 
iiiiiu'l  irraplii.-ally  when  drawi-  -  the  r.'sistaiH'c  lif,.-. 
.Hid.  as  Tar  as  tiie  ardi  itself  is  eoneerned  tlie  lin^^ 
of  i-esistani-e  is  re.piired  oidy  al)ove  tl:e  |)..inf  of 
rnptnre.  It  is.  liowcver.  coiitinned  fnrtlh  \'  .v  de- 
lerniinin-^'-  the  stability  of  the  pier 

Tl'e  folloMinfr  empiric  d  rule  <riv(      approximately 

the   re.inir.Ml   thickness   for  eircidar  sof?ni'    :tal   andi 

rin<rs    at    the    point    of   niptiuv.      Tn    the    idlowinir 

'■-piation   t--^  '-mw-n  thickness.  (/      re(|nired  tliicdiiiess 

at  i)oiiit  of  rupture,  wlieu 

rise  ,     , 

^  '-■         \   tliea  rf  =  2.0(1  t 
span 

~  I  th.'ii  d  --1.40  t 

i   then  d=1.24  t 

V,  then  d     1.1 -)f 

"  ■     ,'iv  then  d     1.10  / 

In    reference    to    the    nee.ssary    thi<  i  !ioss    of   the 

anh  rin<jr  at  varioi'<  points  hitween  tf      crown  and 


i? 


/'/.//"    ''()Xih-/:i  i:  .I'y'if  nh'/iH.i-.s. 


51 


spriii^is  lie  \  (■?•!  leal  |(rujcrt  ioii  id' (>\  iTy  sci-|i<  "  ciif- 
tiM';  l!  aitli  tr  ^  nor  lal  to  lli«>  lin'  of  res  lain-f 
iiuisl  in-  at  li.i-^  as  ;r.  it  a  >  tin;  viTtical  ilcp  h  of 
arch  nny:  at  I '  ■■  crouii. 

Till'   jiositioii    of  tilt    |i(  iiit   of  t'lii    'ire   •."   KTitlly 

<ici'iirs   at    al)(>iit    I  hat     '<)i.  t    of  IIk     ..rcli    wli    re     ''i. 

iiiu'iiial   to   tl'c  I         of   oi        IPC  's  an  anirlt'  of 

t")  ,lcj.Tci-     witli  'ii.    lion      ((I    I.  •  .  liiy  he  sail  that 

t     !M'\r!'    t.iiJM    h,\\\        ih-          i|.     ■  ,-    (if    :{()    (l(;,'n>(" 

N'ith  tlii     h<    i/oiita     a?i             t  hct^v   .'il   '•)')  and 

•i'  (Icjriii's  '    111  tho  j  =1 


i 


y 


Dett  mina      i  of       ah  xhickn 

iiiii'  of  !  -.    ^ui.  the  variolic  points  of 

the  h  1  (  .  .,.f|  (Ictrriiiiiicd.  It  will  bo  soon 
*iiat  tilt  sc   ju't  -sh  icrcasc  from  crow?)  to  sprinir 

ii!    prop,  "lion    to      he    rise    of    tlic    arch.      \n   si 
circiii;!      arches         ■    tlii'ust    at    the    sprin-r    nia; 
'lu'c         foMi-  tlif  thrust   at   the  crown.     'I'l 

•«'l    tivc  pos  11       •enter  of  arch  and  the  lim- 

of  resistant  t   Ix      xaniined   and  suitable   unit 

press^"-es  scic<  -  (1  foi'  she  various  points.  If  the 
liie  ol  -esista  ee  is  at  eitluM"  limit  of  the  middle 
»'     d.  mc,..i  unit  pressure  will  then  be  one-half 

o       h'        aximuin    at    the   outer   edye.      This    is   the 
'!sn  ..     ass  Miipt'  'U.       Then    the    a.Ta     obtained    by 
ividiii','    •■        t "t'l    pressures   by  the   workinsr  units 
will    be    II  ,  lired    an-a    of    nuiterial    at    various 

points  of  ti,.  ;.rch.  .Most  authorities  on  the  subject 
recommend  liberal  sizes,  not  only  because  the  usual 
arch  matei-ial  is  not   expensive,  but  also  on  account 


II 


52 


coxcRiiir.  liRinci-.s  .ixn  criAi'.RTs. 


of  the  iiiKM'iiiiiiity  of  so  many  (■(niditions  iu  (tomicc- 
lioii  willi  the  Avliolc  matter. 

Backing. 

Kcrcrciicc  lias  already  hccti  maile  to  the  point  ol" 
I'upture.  Jt  is  tliat  jxtint  on  the  extra(h)s  of  the 
arch  where  the  joints  tend  to  open,  and  it  occurs 
opposite  that  point  where  the  line  of  pressure  ap- 
|>r()a(dies  nearest  to  the  intra(h)s.  It  is  known  in 
the  failure  of  Hat  arcdies  that  the  joints  open  at  th<' 
intrados  of  the  crown,  and  extrados  at  tlie  two 
points  of  rupture,  and  the  haunches  recech^  later- 
ally, allowing'  the  central  part  of  the  arcdi  to  fall. 
In  onh'r  to  resist  ami  counteract  this  lateral  move- 
ment of  the  haunches  and  apply  horizontal  conju- 
irate  thi-nst  thei-eto.  that  part  of  the  extrados  from 
the  point  of  rupture  down  to  the  pier  is  filled  fren- 
crally  with  l)ackin<r  of  rubble  masonry  or  concrete 
laid  in  horizontal  layei-s.  Semicircular  andu's  re- 
ijuire  ha(d\iii<r  sufTii-ient  to  produce  conjugate  pres- 
sures e(|ual  to  the  crown  thrust.  Segmental  arches 
whi(di  have  a  hoi'izontal  thrust  component  at  th'* 
spring  re(|uires  less  ba(d<:ing  than  semicircular  ones. 

Waterproofing-  and  Drainage. 

Previous  mention  has  already  been  nuule  of 
waterproofing.  This  is  iHccssary  to  prevent  water 
soaking  into  the  joints  and  freezing,  thereby 
teiuling  to  disintegrate  the  masonry.  Waterproof- 
ing is  necessary  also  to  |)revent  drainage  water  leak- 
ing through  the  artdi  and  discoloring  or  otherwise 
disfiguring  the  structure.     To  prevent  su(di  leakage 


PL.  {IX  COXCRIi!  li  JRCIl  PRIDCES. 


53 


it  is  oustoiiinry  to  <'ovr>i-  llic  iii>|)or  surface  of  the 
iircli  and  hackinjr  witli  a  layer  of  bituminous  eoii- 
<-ivte  or  clay  pu. l.!lr.  (  Iny  sliouhl  eontain  enough 
sand  to  pivvcnt  llie  day  from  craekinjr  wlien  dry. 
Walerproofinir  may  he  acfomplished  by  ai)plying  n 
layor  of  rich  moj-tar  and  surfacing  it  with  neat 
•M'ment.  on  top  of  whiidi  is  poured  a  coating  of  tar. 
pitch  or  asphaltum.  The  upper  surface  of  the  back- 
ing must  have  sutTicient  slop(>  to  carry  drainage 
water  1o  tlie  gutter,  where  it  may  be  discharged 
tlirough  pipes  luiilt  into  either  the  arch  soffit  or  the 
side  spandrel  walls. 


Intermediate  Piers. 

In  making  preliminary  designs  of  piers,  use  may 
I)e  made  of  empirical  foiMiiula  to  delerm;ne  approx- 
imate sizes.  Kaid<ine"s  rule  is  to  make  the  thick- 
ness of  piers  at  spring  from  one-sixth  to  one-seventh 
of  the  span  or  arch  for  intermediate  piers,  and  one- 
fourth  of  the  span  for  abutment  piers.  Tntermediat- 
piers  must  Ix-  of  sutTicient  area  to  resist  crushing 
from  the  maxinmm  loads,  and  in  proportioning  the 
base  of  pier  the  weight  of  the  pier  itself  must  be 
lidded  to  tiie  imposed  loads.  Intermediate  piers 
must  also  have  sufificient  stability  to  resist  the  over- 
turning eflTect  of  unbalanced  thrusts  on  the  adjoin- 
ing spans.  Such  unbalanced  thrusts  will  occur  if 
the  adjoini.ig  spans  are  of  different  lengths,  or  if 


one  ordy 

tioiis    the 


IS  sut) 


.jcct  to  live  load.     F 


or  such  condi- 
••enter  of  pressure  shall   fall   within   the 


middle   third    of   pier   baf^e.     Pier.s   must   b 


e   given 


^^oY< 


54 


lOXCh'/ilfi    BRIIH.I-.S   AXn    CriA  liRTS. 


siiflicitMit  sprcjid  sit  the  base,  so  the  pressure  on  Ihe 
fouiulntioii  Avill  ii(»t  exceed  a  safe  unit.  To  neutral- 
ize the  efll'eet  of  unecjual  thrust  on  the  piers  from 
spans  of  different  lenirths.  the  siiortcr  span  may 
have  a  less  rise  Avitli  a  correspond infrly  <r>"<^*iter 
amount  of  fillinir.  This  Avill  tend  to  produce  a  thrust 
from  the  smaller  span  sufticiently  lar<re  to  e<|ual 
that  frcMU  the  loiifjer  one.  Another  method  is  to 
incline  the  short«^r  span  upward  so  the  thinist  will 
act  on  the  pier  at  a  point  somewhat  hij^her  than  the 
correspondiuf?  thrust  from  the  lonnfer  span.  In 
writiiifT  on  this  sul).iect.  Tiankine  says:  "Kach  pier 
of  a  series  should  have  sutlicient  stability  to  resist 
the  thrust  which  acts  upon  it.  when  one  (»idy  of  the 
arches  which  sprinj;  from  it  is  loaih^l  with  a  travel- 
injr  load.  That  thrust  may  I>e  roujrhly  computed  by 
midtiplyinjr  the  travelin<r  load  jxm-  litieal  foot  by  the 
radius  of  curvatui-e  of  the  intrados  at  its  crown  in 
feet.''  The  mathenuiti(  ;d  investifration  of  piers  is 
shown  in  Fiijures  7.  !)  atid  10. 


Abutment  Piers. 

Hridires  havinj;  a  series  of  spa. is  s!  uuld  have  abut- 
ment piers  at  intervals  in  order  that  the  possible  fail- 
ure of  one  span  would  not  cause  the  entire  strnetur'! 
to  fail.  Abutment  i)iers  are  useful  also  in  allowing' 
false  work  centers  to  be  removed  from  some  of  the 
spans,  without  waiting:  for  the  completion  of  the  en- 
tire strucrnre.  AVhen  spring  lines  can  be  located 
close  to  the  foundations,  it  may  be  advantageous  to 
juake  all  piers,  abiitinent  i)iers.     This  was  the  case 


! 

f 


^^S^T 


I'l.Aix  (nxcRiii r.  .\Rcii  nh'/ncr.s. 


55 


ill  llic  loiiiriiuisonry  viaduct  ivci'ully  l)uilt  sit  Santa 
Ana  in  California.  ..n  tlic  liiic  of  the  San  IVdn*.  L(,s 
AiiL'clcs   &   Salt   I>ak('  Kailroad.     (Sec   Enf^inccrinjr 
IJ.'cord.   Scpt.-ndxM-   f).    lOor,.)      Whon    it    is"  inipra.-'^ 
tK'iihlc  to  make  al'  piors  al.utincnt  piers,  it  Avill  tlicn 
1»"  well  to  have  every  third  or  fifth  one  of  the  type. 
Sneh  piers  may  l)e  desijjnod  ^vith  a  factor  of  safety 
iijrainst   overturninir   of   from   one   and   one-half   to 
tv.-o.     Ti   Avill  b(>  noticed  that  the  point  <»f  intersec- 
tion of  the  arch  thrust  with  the  load  line  throu^di 
<Ih'  <-<'nt<'r  of  frrnvity  of  the  piers,  falls  lower  in  the 
;!l);itiiierit  pier  than  in  the  intermediate  ones,  owinj? 
1o  the  irn.ater  width  of  pier.     This  is  an  advantajje 
.hkI  will  hriufr  the  resultant  pressure  nearer  to  the 
••enter  line  of  the  pier  base.     Trautwines  approxi- 
"i;i)e  formula   for  the  thickness  of  abutment    piers 
;'t   11|>  spriniriiifr  is  to  make  the  thickness  c.pial  to 
•>Mc-Mrth  of  the  crown   radius  plus  one-tenth  of  the 
'•ise.  |.  .IS  two  feet. 

Abutments. 

In  proportionin-r  abutment  piers,  it  is  n<»t  neces- 
sary t..  keep  th,>  resultant  pressure  Avithin  the  .uid- 
<il<'  third  of  the  base,  if  the  maxinunn  pressure  al 
t!ie  outer  edse  does  not  exceed  the  allowable  unit 
!>'-essnre.  Trautwine's  empirical  rule  for  the  thick- 
ness (.f  ,  l.u,,,H>nts  at  the  sprinjrs  is  the  sauu^  as  was 
U'lven  ai  ^,  for  abutment  piers.  This  approximate 
siz(^  will  ..  isist  in  establishinf?  the  correct  or  tinal 
one  and  the  rule  gives  a  thickness  intended  to  be 
sufficient  without  depending  upon  the  existence  of 


■MMi^fll 


56 


coxcrhth  nRinciis  .ixn  cri.i'HRTs. 


earth  ])iv'ssuro  from  Ix'liiiid.  Ahntmciits  siisliiiniii<? 
liiirh  hjiiiks  of  loose  iiuiterisil.  must  lie  proportioned, 
not  only  for  the  areh  thrust,  hut  also  as  retaini!i<,' 
walls. 

There  is  fre'|ueiitly  mor(>  masonry  in  the  abut- 
ments of  a  bridjxe  than  in  the  span  itself.  For  this 
i-eason  it  is  desirable  to  consider  carefully  any  op- 
portunities for  satiny  nuiterial  in  the  abutments. 
IMacinjr  the  arch  sprinj;  down  mar  the  ^n-ound. 
•rreatly  reduces  the  ovorturuiiifr  moment  on  the 
abutnu'nts  and  causes  ■,:  considerable  savinj?  of  ma- 
terial. Tn  brid<rcs  Avith  several  arch  spans,  even 
thouprli  the  spring,'  lines  on  the  piers  must  be  hij;h 
to  secure  a  clearance  undei-neath  tlu»  bridfje.  the 
s|)i'in<rs  at  th<^  end  abutments  may  sometimes  be 
kept  down  lower  than  the  correspondiufi  sprinjrs  on 
th(>  pi<'r.  (  "  if  abutments  must  be  hiirli.  it  may  be 
ect)nomical  to  use  ribbed  ab\itments.  cored  out  and 
reinforced  with  metal  bars,  if  necessary. 

The  use  of  ])avement  ties  of  either  wood  or  metal, 
will  cause  the  arch  thrusts  to  counteract  each  other, 
and  thcr'>by  ijreatly  reduce  the  size  of  abutments. 
This  (expedient  has  not  been  used  to  any  jrreat  ex- 
tent until  recent  years,  and  even  now  is  used  cdiiefly 
for  bridijes  of  reinforced  concrete. 

A  wide  and  shalloAV  waterway  is  more  etfeclive 
than  a  narrow  but  hitrher  one  of  the  same  area.  Fi<?- 
ure  11  shows  some  possible  abutment  forms.  At 
A  and  ('  are  shown  abutments  where  the  concrete 
in  front  of  dotted  lino,  not  only  is  of  no  swvice  or 
benefit,  but  actually  decreases  the  area  of  waterway 


'I'^i.  Wi'ST 


V9r»»«»j 


/7..//.V  COXCRllTr.  ARCH  HRlDCrS. 


57 


{111(1  at  tlio  samo  tinio  adds  1o  the  cost  of  the  stnie- 
tiin'.  It  Mill  bo  seen,  howovcr.  that  the  abutment 
A  is  one  of  the  most  eommon  forms  used  in  nearlv 


Fiir.  11 
AK(  H    AUl  TMENTS. 


all  old  andi  brid^'es.  If  fm-  any  suffieient  reason, 
vertical  sides  are  desirable  or  neeessary.  it  will  be 
eci.iiomy  to  build  independent  side  walls,  as  shown 


: 


•'■•8       (owRijh:  liRiiH.i-.s  .i\/>  (i/.r/:h'Ts. 

at   J5.    rati.,.,,    ll,,,,,    w„sl,.    .M.-.l.-rial    l.y    uu.kii.jr   tl.o 
wliolc  iihiitniciit  solid. 

Al  K  an.  sli.nv.    „|,1  ami  n.-w  nidlKMis  of  const ni.-- 
tKMi.     The  (lottcl   Ii,„.,s  sliowinjf  an  al.utni.M.t   l.iiii; 
'""  l<'V("]   fonn(lati(.n   is  die  inctlio,!  j;ivi'n  l.y  Traiit- 
winc  and  tlic  one  .generally  uscl  ii.itil  riMM^nt  vcars. 
Tt  will  l„.  scMMi.  li<.w..v(M-.  that  the  f,.nns  shown"  at  K 
".   full   l.M.-s  is    oinally    ..ffVctiv,'    in    trans.nittin-^ 
thrusts  to  tl...  soil,  a.i.l  r..<,nir..s  somewhat  less  n.;i- 
t.'nal.     11    vertical  si.les  are  not  re(|uire,l.  son.e  a.l- 
«  'I'nnal  ...aterial  ,„ay  he  save,]  hy  „.sin-  the  ...etho.l 
shown  l.y  ,lott...l  lin,.  at  ('.     1)  is  suitable  for  arelu-s 
M-.lh   e,.nsi,l,.ral,]..   ris,.   on   har,l   soil   ,„•  loo.se   ro,-k 
an,l  Fslmwsa  l\m,^  of  ahutni.Mit  in  whieh  th,'  an-;, 
thrusts  ayainst  s,>li,I  i-oek. 

Tm  (l.-sifrnin-  abutments,  it  is  saf,.r  to  ,lisear,]  the 
•'tt.'et  of  e,.n.,uv„te  .-arth  pressure  on  th,'  ar-h  ex- 
tra(l,.s.  The  al.utm,M.ts  will  then  h,.  sonunvhat 
heav„-r.  hut  the  error  will  be  on  the  side  of  safety 
Jumkin,.  says  that  the  [hiekn.-ss  of  abutments  is 
••ft,.n  from  ..n,-thir,l  to  ,.ne-fifth  of  the  ra,lius  of 
••urvatur,.  at  the  en.wn.  Flarinjr  wing  walls.  2.-)  feet 
in  h,.,irht  or  less,  rigidly  e,.nn,M.ted  to  the  abuf.u.Mt 
tae,.  wdl  or.linarily  !.,■  safe  with  a  base  e.,ual  in 
NVi.lth  to  on,.-fifth  of  th,.  h,.i.},t.  This  is  ,.ulv  half 
|l'"  thH.kn,.ss  usually  giv.M,  to  retaining'  walK  and 

''    '""'    ' ■■'"^'"    «'f    <1"'   an-ular    ,-onne,<tion    t,.    th.> 

Jtbutment  face. 

Foundations. 

riors  and  abutments  must  have  suffieient  spread 
»t  th..  bas,..  so  th,.  lua,l  on  th,.  f,.undation  will  not 


s 


I'l.AIX  COXCRHTE  .IRC/ 1  imiDCF.S.  59 

';xn..I  a  safe  unit.     For  s.,il,  this  will  not  ordinarily 
•X-..1    nun  two  to  fonr  tons  jn-r  s,,uaro  foot  at  the 
"-.-••  ,..I,.o  of  the  pier,  where  pressure  is  the  .nvat- 
-^  ■     n  p.les  are  used,  the  same  precaution  will  b. 
•''-';•     Slop.njr  piles  have   o.vasionally   been  useu 
"   "  .-h   foun.lat.ons   for   resisting   the   areh    thrust 
I     the;,'   are   n.ore   diffieult   to   drive   than    plumb 
I   hs      Th.   Jan.estown    Exposition     bridge.   Figure 

•'•''\"^'"t-  "...  .uaxunun.  allowable  load  on  piles 
sl.ouhl  not  exeeed  fro,„  1.1  to  2.1  tons  eaeh,  depend- 
".g  upon  tlu.  penetration  of  the  pile  at  the  last  blow 
;;'  \'-  ';'""—••  AHowanee  nn.st  be  nu.de  for  the 
■'■s..ltant  pressur,.  on  the  base  falling  outside  of  the 
-''••<••  Tt  need  not  .H-eessarily  be  eonfi,.ed  to  the 
■<''"<'  n..nl,  p,.ov.ded  the  pressure  on  the  founda- 
1"'"sar  the  outer  edge  is  not  excessive 

In  h,s  treatise  o,,  Masonry  Construction,  Profes- 
•s-r  Ii*.l<.r  giv,.s  the  following  values  for  safe  bear- 
ing p.»wcr  of  soils : 

Tons  per 

Rock  e^ual  to  best  ashlar ""^Tto^'io 

Rof'k  .qual  to  best  brick  .nasonrv.  ...  "  " "  'n  to  ?0 
Rock  ec.ual  to  poor  brick  n.aso,.'rv.  .  .  .W"  :,  to  10 
Hay,  dry  thick  beds "  "   [  J^^   ^[, 

Clay— n,()de,-at.>ly  dry  thi.-k  Ix^ls o  to     a 

Clay— soft     "  "^ 

^ii-avel  and  coarse  sand  well  cen'.ented .'.'.' "   8  to  10 

^and-er,n.i,act  and  well  .emented 4  to     (i 

Nand— clean  and  dry  .  .  o  t        • 

Quicksand,  alluvial  soil    etc     , "  .       , 

'  •>  to     1 


m 

I ''  I 

hi 


«0  COXCRJiTi:    BRinCl-s    AM)   Cri.lERTS. 

Expansion. 
It  is  well   to  provi.lc  for  possihli-  expansion,  so 
cracl-.s  will  not  appear  in  the  finislied  surface.     In 
til.!  ease  of  the  Conneelieiit  Avenue  i5ri(|<re  at  Wash- 
ington, shoM-n  on  pa<rc  SS.  onr-haM"  inch  expansion 
j(ints  are  provided  thronjriiout  the  entire  hei<,dit  of 
th.i  spandrels,  from  sprinj,'  to  the  ll.x.r  over  the  ])iers 
and  across  the  roadway.     These  arches  are  150  feet 
in  len«rth   and   semicircular.     After  the   completion 
of  the  concrete  arch  hrid^'c  over  iJijr  .Muddy  Kiver 
on   the    Illinois   Central    IJaili-oad    /See    I':n<rineerinfr 
.\<'ws.    .Xovemher   12.     VM):\)     an     examiiuUion     was 
made  durin<r  a  i)eriod  of  several  months,  and  almost 
no  expansion  whate\er  was  discovered. 

Surface  Finish. 

Various  methods  have  been  ad<.pted  for  procnrini? 
satisfactory  surface  linish  on  concrete  structure! 
Among  these  methods  may  be  mentioned  cement 
washing,  tooling,  sand  blasting,  rough  casting  or 
slap  dashing,  scrubbing,  cold-water  painting. "and 
acid  treating.  The  Connecticut  Avenue  liridge  at 
Washington  has  corners  and  moldings  made  of  con- 
crete blocks,  and  to  remove  form  i:;-.rks  the  body 
and  tiat  face  work  were  bush  hammered. 

The  Walnut  Lane  Uridge  at  Phihulelphia  has  a 
rough  surface  finish  similar  to  pebble  dash,  but  of 
coarser  grain.  Tin.  surface  shows  stone  chips  not 
larger  than  thre.'-.ighths  of  an  inch  in  diameter, 
lornied.  by  washing  the  concrete  face  before  the  ce- 
ment had  har.lened.     A  more  expensive  method  of 


§3,V^:^^^^^ 


5'V'^vOS 


/7..//.V  Co.XCh'/iTJ'   Aiail  HRinCES. 


CI 


K 


•s-Minnjr  a   fitiisl...,!  surfiKM-  is  to  build  all  oxposed 
siirla.M's    ,.f   ,-ut-st()ni.    work,    or    a    .M.inhi.mtion    of 
stoiu'  and  brick,  usin-  coiicrct."  Tor  the  body  of  the 
Wyi-k  only.     Till.  (ircMi    Island  Concrete  Hridgc  at 
Xiairara   Kails  l,as  surfa<-in^'  <,n  the  spandrels"  and 
pi.-rs  of  cut  stone,  and  other  bridf,'es  have  been  simi- 
larly bnilt  at   Indianapolis    and    elsewhere.     :^Iany 
hridfres  generally  known  as  stone  masonry  bridges 
are  stone  only  on  the  surface,  with  the  body  of  pu^rs. 
arch.'s  and  backing  composed  entirely  of'  co.H-ete. 
The  Rocivville  stone  arch  bridge  built'  by  the  Penn- 
sylvania  TIailroad  Company  over  the  Sus(iuehanna 
Kiver  IS  of  this  construction.     Tt  has  stone  facin*' 
thnrnghont.    including    the    soffits,    spandrels    and 
pH'rs.     [n    budding   an    ornamental     concrete     foot 
bridge  over  two  lines  of  railroad  at  Como  Park.  St. 
i'anl.  to  avoi<l  the  appearance  of  form  marking  on 
the  finished  surface  of  the  bri.lge.  the  entire  surface 
<»t  the  lagging  and  -noulds  was  lathed  and  finished 
Avith  fine  plaster.     In  tlie  National  Zoological   Park 
^^ashlngton.  is  a  concrete  bridge  faced  on  the  span- 
drels and  parapets  with  natural  boulders,  which  ex- 
tend down  s;x   inches  or  more  below  the  concrete 
soffit.     In  San  Francisco  are  .several  concrete  brid-rps 
Avith  rustic  surface  finish,  made  to  represent  natural 
bonlders.   but    really   fonncd   of  moulded   concrete 
These  boulder  and  rustic  surfaces  are  appropriate 
tor  certain  wooded  pai-ks  or  rural  places,  but  are  not 
isiiKable  for  general  adoption. 

Engineering-Contracting  for  January  6,  1909,  con- 
tains dlust rations  of  concrete  surface  effects  secured 


\v. 


V      '^      X      _       .      _ 

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_      -  i.  CC    „  "      0- 


cd 

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c 


—  _^  -  f"  -t-  —  C- 

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r  _z  -I  c  c  ,£: 


v.     w 


=    -    =    r  "i  «*-!  's^ 
-    ~    =  -=    ?    c  j: 


?*--  .r 


3ifii^. 


/•/.  //V  tY>.VC,V/r/7,  ./A',  //  HuiiH.l.s  ,;:] 

l>y  v„ri..M.s  „M.tl,<Mls  „„  lahon.tnry  samples.     It  will 
•"  'm,l..rstno.L  iM.MM.v.r.  tlw.l   h.iWv  .vsulfs  ^umh\ 

' '''"""'•'  "•"'"»•  <1'<'^<'  <'on(litions  than  cnnl.l  1 x- 

IM'ftcl  o„  larir,.rs„rr;MM.s  mI,..,v  <„„.  of  its  ,.l,i..f  .lini- 

••iilfi.-s  IS  to  j)n)(lti(M>  iitiifonu  cfTccts. 

Sto„y  IJrook   Itri.li:,.   i„  tl„.  iJostcu.  F.Mnvavs  l.as 

frramt,.  tnn,„ii„irs  m  tl,  spn-rkl,..!  Lri.-k  fa.-in-  whil.- 

I""  •"•<•!•  ^"Hifs  aiv  linnl  with  -Ia/<.,1  hri.-k  of  varv- 

I'ly  pjitlcnis  and  colors. 

''''"•;••'  i;<  i<  very  artisti.  thn-.-spa,,  an-h  hrLlfro 
:'\"'-/  '<'  nv.r  at  I)..s  Moi„,.s.  Towa.  that  has  vitnfir.1 
'"'"•J^'  :'-"^'.  Th.  spans  a,v,.a..hl..(MWti„h.„.,h 
"':''  '■"'''."••"'  '■"<■'"•'"•  'H...  hri.-k  nn-inir  with  tri.M- 
"""jrs  ol  a  Iij,h|.T  ,.olor  p,,.s,.nts  a  v.-rv  pl.asi,,.. 
iipp<'iii'ann'. 

Anoth.-r  ,n..tho,i  of  prcv.M.tin-  forn,  marks  fron, 
;''•'•"*"'■'"-  ""  <'"■  •••UMTot..  surfa.M-  is  to  ,.ov,.r  th.- 
l."-'i:.nir  with  a  lay.r  of  fi,,.  Hay  an.l  ov.vUy  tho 
siuiic  with  bnil(liri«r  paper. 

Cost  of  Concrete  Arch  Bridges. 

The  cost  of  coacrPto  IumM-oh  varL-s  witl,  l,.ral  rr- 
Munvn.ents  and  conditions.  The  foll-win^^  ori.nnal 
;'nnn]a.,vcsthccostnfs.  Id  concrete  arch  h.-id..,, 
^'l•    Ix.th   railnrnds  and   liii^hways.     The   fonnnhfi. 

^  ~   *  \  100  y 

where  C  is  the  cost  in  doHars  p,.-  .sc^uarc  foot  of  road- 
^^ay   H  tlie  ^.encral  heii,d,t  of  the  hrid^r^  at  the  center 
^^  the  total  widtli  and  F  a  vari«l,le  factor  givn  by 
the  followinj,Mable:  • 


64 


((>\t  h'i:i/:    nun 'I. is-      IXf)    (7  7,;7:A'/'.V. 

When   A  is       •^»()(i.   tli.-?i   !■'  is   I..-. 
.">(»(  I. 
I  (Kin. 

•.'()(  11 1. 

.'.Mm.      •■ 

."lood. 

;i;.(t(i. 

1(1(10. 

:.n(i(».      •• 

Cdoo. 

;(i()(l.     •• 
••        ••        soon. 
'•       '•      :i(i(M».     •• 
1 1  num. 

••        !1(I(M.        • 

I  •.'(»(  to, 

i:;o(i!). 

••      I4(i<:;).      ..       .. 


As  tlw-  lH..,,ht  .,{•  i!,..  ]>rll:r  ,nulii,.li,.,l  l.v  its  wi.ltl, 
.rnt-s  flu.  cn.sss.M-ti.mal  aiva.  tlir  fuMcti.,u  HW  mav 
he  ivinvsont,-,!  hy  tlu-  l.ttrr  A.  Factors  V  ivtVr  to 
an-hl.n.l.vswith  (■on.j;l..t..  soffit  slahs.  wl,il..  factors 
1'  refer  to  an-h  l.ri.l.vs  with  partial  soffit  slabs,  such 
as  used  m  the  Walnut  Lane  l.ri,l-^e  in  Philmh-lphia. 
'in.lthel),.tn,it  Ave.  hrid-e  in  ( •l.-v.-lan,!. 

The  eost  of  concrete  l.ri.Jircs  is  atrccted  more  by 
natural  conditions  an<l  the  sele.-tio.i  of  the  economi;. 
torn.s   than   by  the  live  load  to  which  these  bridges 


.(» 

.<;:. 

.IS 

.4-2 

.;;<; 

:;•.' 

.•js:> 

.  ■.•(;•.' 

and  !•"' 

is  .m; 

•.'•J  I 

.. 

.'.i:» 

•.'!• 

..     .. 

.!•! 

IS 

.. 

.;i;; 

\m 

.. 

.'.fv* 

l.v.' 

..     .. 

.!il 

Ill 
i;!:! 

•  • 

.  ss 

.Sli 

1-:.-. 

.. 

.S.") 

11  :• 
ii:; 

;.■ :: 

.SO 

■msm,^ 


kr. 


/7..//V  iOXCh'/m.   ./A'(  //  HRIIH.ES 


6 -I 


nrc  siihj.clfd.  This  is  sliowji  liy  tli.' al».vi' fonmilH 
.•ipplyiii^'  <M|ually  to  (-(.iicn'tr  jirdi  bri(l;,'t>H  fur  Ii..fh 
r.iilntads  and  !ii;;liways. 

TIk'  w«'i;rlit  of  concnli'  and  (itluT  niati'rials  is 
•rrrafff  than  tlic  iiiipos.-d  live  load  and  tlif  live  loads 
.••If  not.  tlit'n'forc.  fr,'  chiff  caiHid. -rat ions  in  drter- 
niinin;,'  tli.'  ultimate  ('(.st. 

Tli.>  formula  clrarly  shows  that  conrn't.'  anh 
l»ridurs  vary  in  .(•st  in  ])roi)ortiou  to  th.' jn-.Kln.  t  of 
th.-ir  w.  i-rht  and  width.  Bridjjrs  with  a  small  m.-sH 
st'ctioMal  arra  cost  as  low  a  price  as  J!2.ri(>  jmt  sijuan' 
foot  of  tloor  surface,  while  lar^re  monumental  hridfres 
may  cost  as  liiirh  as  510.()0  \)vr  sciuare  foot. 

The  formula  also  ch'arly  shows  the  ^n-eat  ectmomy 
in  nsinjr  ])artial  in  place  (.f  com{)lete  sotfit  sIh})8,  nnil 
tliis  economy  may  be  still  further  increased  by  the 
us(  f  ribbed  arch  (h'si^m^  ^fl)l)ed  an-hes  are  not, 
how.  r.^'enerally  suita))h  1,^  ^^tructi.m  in  solid 
concrete  and  the  treatment  .w  l!,;,-,  .  tyle  of  an-li  will 
ti  .refore  l)e  taken  up  later,  >  i',.  i],,  desi.irn  of  arches 
in  reinforced  concrete. 

Table  No.  1,  jrivinjr  details  of  concrete  brid.ires, 
j,'ives  also  tlie  total  cost  of  these  structures. 

Design  for  a  Concrete  Arch,  60  Feet  Center  to  Cen- 

ter  of  Intermediate  Piers.    Clear  Span  53 

Feet.     Rise  10  Feet. 

The  hi  idgo  consists  of  a  series  of  arches  to  carry 
a  street  over  a  number  of  railroad  tracks.  The  span 
y,-as  arbitrarily  fixed  at  60  feet  center  to  center  of 
intermediate  pi.  rs.  or  53  feet  in  the  clear.  This 
provides  clearance  for  four  lines  of  tracks,  13  feet 


<;<; 


coxcR/://:  nianciis  .i.\/>  cri.irMTs. 


"l-'o„  ...„,..,,.   l-'ur;,  Wsln,..t,nvuni.isl.,.i.l,t 
1^ -.•  -  sp;u,s  Mn.ht  lun-o  lKv„  „.Hv  ,vononn..I.  l.„; 
-s  I....tl.  w.s  sHn.,..,  tl:.t  tl...  ,.I..nra„,.,.  whv  for 

•■;•-;  <s"-nI.lM.,t,,,.  too  .n.,tlyol,stn.,.t..,l\viti. 
'     '!•      """  ''"'•'<'••"•'">  un,l,.nH.,f|.  is  shown  .m  Fi.-- 

|-«-   s,..,,H,,tinMs.lH.i„,,21  f,..tfroM,thMnp;,fraiI 
"'    "'."  -'"<"'•  "f  tnu-k    n.nnvsf    to    tl,o    pi.r      Tin- 

;''Pt;-MV>rn,  was  s..]..,.,,  for  th.n.nson  that,  with 
-  ^iv..„  H..,,-a,H.o.  it  alhnvs  the  spHn^i,,.  li,..  to 

.^1     Wr  than  any  oth..,-  fonn  and  i„   this  .aso   is 
'•'♦"r/"'*"^"''"'^"-'"""!-     ^Vs  tho  via,lu,.t  is  a  lon.^ 

V     ;, ;'  ""","""";  '•'^"  ••^'  -"-fif^'^  the  spa., 

A\...s  th  n.fon.  s..l..,.t,.<|.  anionnfin,.  to   10   f.-ot   front 
;|;;.-    o  ..-own.     Th.  Hs.  is  tho  s.ni-n.inor  L     : 

P  -ssn,       whH-h    ,s    „s.Ml    h,t.M-   in    dotonninin^   th. 
"•-owti  thrust  an,]   [,i,.r  reactions      TI. 
rule   fui-  tl„.   ii-  1  "'"Tions.      I  he  approximate 

'.;;•'.    '"'•'<--   of   intennediate   piers    is   to 

iH      1;     •"";'"•' ^'""-     -r'- -onid  produce 

^t    hK„,,,,,  ,,. "toSf.vtatthesprincand 

'    ^-^  ;^-^  -l".-t..<l    i-or  a    trial.     To   detennim. 
"l>I';-nnate    crown    thickness.    K.,d<ine's    .T  ^ 
•;^^;<1-     K.ra   series  of  .rches.   it  is       ,.17  Kadius. 

Ths  rcp.ires  that  the  radius  he  known.  I.av  out  .,n 
:  ;;-^'-=.;i.-myhyn.  n^thodoftive'c:^^^^ 
•""f  ^''"  -'Jnis  ,s   found  to  he  72  feet.     Rankine's 


i 


/V..//.V  COXCKliTIi  ARCH  /BRIDGES. 


rule.  ;i.s  iil)()\ 


('.  <r 


n 


\\i's  }i  thickness  (.f  ;}.:,,  wliih,  Traut- 


ine's  rule  f„r  the  Jipproximatc  thicl. 


kncss  IS  L'lvcfi 


.  «' •■■•■••■'       lUM-KIH-X.S      IS     jL,'IV(MI 

m  Ins  book.  paj,^.  (il7.  and  is  2.2  feet.  Try  a  thick 
lu'ss  of  2..-;  f,.,.t.  Tho  jrradinj.  of  fh.  hri,!?.  „p  to  n 
hifrhcr  lev.)  in  onh-r  to  sc-ure  a  -n-ator  ris.-  for  the 
i>rch  was  consider..!.  h„t  as  this  increase!  the  (,uan- 
tit.-s  of  ,„atcrial  i„  the  superstnicture.  and  would 
<'(.'H.t  a  savin-  only  i„  the  abutn.ont  piers,  the  pbn 
was  not  adopted.  A  thickness  of  crown  fillinfr  of 
2..)  foet  was  assuniod  from  the  extrad(.s  of  the  arch 
to  the  pavement  surface. 

The  entire  portion  of  the  hrid-e  j.hove  th<'  intri- 
dos   was   then   divided    into  strips,   and   the   weif,.ht 
for  ,.ach  <.f  th(.s,.  strips  calculated,  on  the  assumn- 
t.on  that  earth  fillin,^  weicfhs  100  pounds  per  cubic 
f'H.t.  and  masonry  IfiO  pounds  per  cubic  foot.  A  livo 
load  of  l.-,0  poun.ls  per  scp.are  foot  was  assumed  on 
th..  roadway.     The  w.Mfrht   was  .-ompute.!  for  each 
stnp   and    noted    on    Fi-ure    7    in    their   respective 
places.     The  a.nount  of  con.ju-ate  thrust   was  then 
fo.ind  by  taking  the  intensity  of  such  thrust  at  one- 
th.rd   the  weip:ht   of  earth  and   live  load   above   it. 
These  wer(>  also  noted  in  their  proper  places.    re,.t<-r 
lines  wer..   th.Mi   drawn    throuj;!.   each   strip.   an<l   a 
load  dia-ram   constructs   by  drawin-  in  (,rder  th.. 
various  vertical  and  horizontal  loads  from  A  t..  P. 
as  shown  in  Figure  7.    A  trial  pole  P'  was  selected 
and  lines  drawn  conn.M-tin-  each  of  the  loa<I  points 
on  an  with  P'.     The  corresponding  funicular  poly- 


•mBr^'^iif^mrmirfim''i 


If 


! 


r.s 


COXCRllTE    BRIDCrS   AM:   CriA'HRTS. 


fron  ay  wjis  dnnvn  with  lines  pan.llol  tc  Iho  linos  in 
the   n.ree   p„lynron   AI".   BI>'.  ,.te.      This   is  ..vi.lontlv 
not  the  correct  position  of  tlie  pole,  for  the  result- 
injr  fnnicular  poly^^on   lies  ahnost   entirely   outside 
of  the  arch.     Hy  i)rolonjrin<i  the  last   string  of  tho 
funicular  polypron  f,,  its  intersection  at  ^  with  the 
horizontal  throiifrh  the  arch  center  from  a,  wo  find 
the  point  of  application  (.f  the  resultant  of  all  the 
imposed  loads,  which  is  at   -.     The  direction  of  th.. 
resultant  pressure  would  he  jiarallel  to  AB.     As  tho 
positi.Mi  of  this  point  is  constant  for  any  other  posi- 
tion of  pol,..  we  may  draw  throu«rh  v  a  line  vt;.     This 
will  represent  the  direction   of  the  actual  "pressure 
of  the  arch   on   the   abutment.     Throujjh   R    in   the 
force  polyjron  draw  a  line  parallel  to  v^  intersecting 
the  horizontal  throu-h  A  at  P.     Tho  point  P  will  be 
tho  correct  position  ^^f  the  pole,  and  the  distance  AP 
measured  to  the  same  scale  as  tho  line  AP.  will  rep- 
resent  tndy   the   amount  of  the   crown   thrust.     In 
this  case  it  is  42.000  i^ounds.     This  investigation  is 
for  a   portion   of  th.-   bridpr    one   foot    in   length  at 
rijrht  an?les  to  the  dia?ram.     Pressures  at  the  var- 
ious points  in  th(^  ;irch  correspond  to  the  lengths  of 
hues    in    the    fore-    j)oIyjro,i.      At    the    pier    for    full 
loadmjr,  the  pressure  is  4S.000  pounds. 

Uneven  Loading, 

Tiines  of  resistance  wer-  next  drawn  f,,r  unsym- 
wietrical  loadinir  ;is  shown  in  Fi<jure  f).  This  has 
.ilieady  been  .piite  fully  desenbed  under  the  head 
of  I'artin!  Loads. 


/'/..■//.VrO.VC-A7:y/:   ./A.r///^A7/.(;/:.V. 

Required  Area  in  Arch. 


ti!» 


Tsin-  n  niaxinuun  prossuro  (,.f    400    p.,,,,,,!.    ,„.,• 

SMnar.HM.h.sas.fowoH<in.unito,...o,K.n.t,.. 
t'-n.ter  ed.e,  or  200  pounds  p..  s.n..n>  indMn..;;, 
P>-..ss„n..  tlH.  n..,uin..|  ,„•..„  i„    tli,.    .n-h    is      :^'"i!i' 

or21(,s,uan.i,    „         'Hus  r.,uU:s  .,  ,.,,u  „r  'Z. 

lo  'r       .,"'""' ^''"■'•'^^•''■^•^•'' "<i-pti...r 

^N.thaaopthof:50in,.hos,thomoaMpn.s.s,n „  tin.' 

or  the  200  pounds  whidi  is  propos,.,!. 

Intermediate  Piers. 
II'"  ar,-h.s  ,„„l  tl,..  livo  l,„-„l  is  .-,4.0,,,,  ,„„„;       '"" 

:;7",'™""- -ii- Mo,,,...,,,,.... ,"'  i,i,- : 

"'™f"^  """  I"--"' II,.-  o„„., ", 

MT-Hss,,,,,..  ,„„r„f  „,«„„„„„„    „^,„;l'^ 
'""  I"  "I'^l- lil-'''-t  loil.ls  is  lli..|-..f.„,.       -1"^" 


(ir 


"';"'™"-'-""|<i"'s'"v.-n,i„,..„,„i,i,.,.„i '"- 

thr,'.'" '''"*■'!''■,'"" '■'■'■''"'''''I"''- 1'"" •-'".. 

«,tl.  .U-a.l  l„a,l  „„|y.    Tl„.  ,i,r„s,s  i,i   ,l,vs,. 


.^ 


If 


TO       co.vt'A'/://:  nKinai-.s  .;.\7>  cn.rnRTs. 

Iwo  cMscs  jirc  4?<.()(l(»  j)ii(]  42.000  ixmiikIs  respectively. 
'I'lii'  lotiil  liijul  (Ml  11i(>  pier  iit  llie  li'vel  (if  tlie  fjtrouiKl 
is   I  Ik  jM'Tcn     ;is   lollows: — 

rounds. 

I'r<!il    I'lllly    l.i;iflc(l    sp;i'i 2ti.000 

I''rniii   p.'irtly  Injidcil  span _':!.000 

Wei^'lll    nf   pier    IS. 000 

Tni;il    t;i.(H)n 

l>y  (■(iiiil)iiiiiii,'  iliis  lo;i(I  witli  llic  iii'clr  tlinist .  we 
liiid  Hie  i-'siilljuil  prcssi:iT.  1]  ,■  lim.  of  which  inter- 
sects thi'  li.-jsc  at  irrmilKl  level  one  foot  Troiii  the  ceii- 
t''i"  <'t"  tlie  piei-.  which  is  well  within  the  Mii<l(lh' 
third.  This  icskII  ii;ay  \  ei-y  easily  he  ehe(d<e(l  aiiii 
lylically  The  width  d"  piei-  at  hase  is  II  feet,  whieli 
was   i'oiind   as    rolhiws-    - 

The    tiital    pressiil'e   i  n    t  he   Sdil    is  : 

Pounds. 
From  lit  idu'e .")4.()0() 

I'"riiiii  piei-   27.000 

Tnial    S1.000 

-Mliiwin^''    a    mean    pt'essure    ol'    (i.Od!)    pdnnds    per 

S((iiare   foot  on  the  soil,   the  iVMpiil-ed    width   of  piei'   is 

SKHK) 

-      ,,        "•'   1"^'>    feet.      If   the   soil    will    not   sustain 

(IdOO 

•  i.OOu   pounds   pel-  sipuire    foot.   wlii(di.    allowiii.ir    I'm- 

uiiexcn   pressure,  crpials  4  to  .')  tons  per  sipiare  foot 

ilt    the   outer  edye.   piles    will    then    he   I'etpnred 

Abutment  Piers. 

In    i)ropo!'tiotiiiitr   the   ai)iitiiien1    pier,  st.ihijity    is 
the  (diief  coiisidei-atioii.      It    must    he  stahle  aj^amsl 


I 


/V..//.V  COXCR/n/:  .iRC/f  HRinGIiS.  71 

tlic  Ihnist  of  arch  from  o.io  side  onlv.     This  arch 
tlinist  intcrsocfs  tho  .M-ntcr  of  fh."  j.i.r  at  a  distanc 
"f    U    fcot    al),»v.>    the    -r<,„„,i.     Tho    ovorturninf; 
I'lonicnt  from  this  thrust  is  therefore  ."^OOOXH.  foof 
l-MMuls.     rsinjr  a  faetor  of  one  and  one-half  against 
"verturnuie.   th.'   neeessary   moment   of  stability   is 
•Ti.OOOXHXi,:..  ,,  ,n.,oo  foot  pounds.     Next  pro' 
<-"<'d  to  tind  the  half  Avi<lth  of  pior  base  at  -round 
l"vel.     fallincr  this  half  width  x.  the  re.juired  mo- 
iiuMit  of  Stability  in  foot  pounds  is 
^i:mOx+{'lxxnxm))x-    .;!..;{00  foot  pounds       In 
tli"  above.  22  is  the  totnl   JH-ijrht   of  the  pier  from 
til.'  top  of  the  -round  to  th-  top  of  the  baekin-   and 
K'O  IS  the  weijrht  of  the  pirr  material  per  .Mibie  foot 
1-rnm  the  abov.>  we  obtain  a  .pundratie  e.|uation.  and 
sulyuM'.    we    find    the    vnlue    of    .,-    to    1„.    8.4:.    feet. 
This  would  br   for  a   pier  with   vertieal  sides      r.,r 
Nb.l>injr   sides,    take  a    half  width   at    the   base   of   !) 
<'"•».    as   shown    in    Fi-ure   !>.      This   siz.>   .,f   pi.-r   is 
tlieii  amply  stable  ajrainst    uerturnin- 

<'<'nn,ir   .M.t    Ihe    haunehes    by    means    of    i„f,.Hor 
spandrel    w.lls.   w<.uld  <"vid..ntly   W  ,.,  ......m.mv   in 

so  flat  an  an-h.  The  eost  ..f  snrh  walls  and  nrehin- 
^^"••1,1  b..  -reater  than  th..  savin-  m  the  areh  rin- 
l.-.n  the  redueed  dea.l  load  and  the  b-ss  amount  of 
nllin-. 


Illustrations  of  Concrete  and  Masonry  Bridges. 

''''.e    fon.-oin-   ta(,b.    -ives   a    list   <.f  areh    bridf,es 
^''"  •"«•""  anl,,s  of  which  are  built  of  solid  eoneret..' 


r  ' 

1 1  , 


)  * 


'-  (('Wk'l.T/:    lU<llH,i.s    .l\/>    Cri.lhRlS 

witlinut  iiiriiil  iviiiror.M.n,..,if.     Tn  ono  cf  tlK'sc.  Iiow- 
"v.'f-flir  n,iln.,„|  hri.!-.'  oviT  tlic  Vcnnilli.^n  Kiver 
;it   I);mviII.-— iTinrnrc..nH-ii(  w;is  jicliiiillv  i-scl  i,i  fho 
'"••""  '"-Hi.  hut  w.-.s\-,<I,.pf,,l  ,,„|y  for  111,.  ,„n-i...s..  nf 
Ix'tt.T  iniifin-  fl,,.  ..uM.Mvtr  .-uhI   pn.v.Miti„jr  n-M-ks 
''••""    ••liaiiir.-    of    1..ni|...|-;,tmv.      In    s.-v.-nil    ..f    f|,.. 
'•*'"''■  '"•i<l^«'"<-   nni,.,I   i„   ,|,.,  i;,i,J,,   „iHi.l   .■.■infom>. 
""•nf   W.MS  ns,.,I   in  spiui.lrrl  ;,.vli..s.   ,„•  ofli,.,-  ininoi- 
P"i-ts.  hut   ns  .•iln.Hly  sf;,l..,I.   tl...  .„;,!„  mvlM.s  lu,v.. 
'>•'••"  •l"siu-n.Ml  ^vitl,   UM  pruvisi.Mi  for  tension  in  i.nv 
part   .,1    tl„.  .,n-|,  s-.-ti-.n.  .•.n,I  .-nnsniu.M.tlv  no  n-cil 
i:<.r  iTuitoivin-  nictiil  to  ivsist  .Iiiv<-t  stresses. 

Tlie  tiil.le  is  not  intend. ',1  to  I,,,  coniprehonsive  or 
Oninplete.    hnf    uHves    so„,e    .jetnils    of    ;,     few    ..f    tile 

Jnrirest  .-onen-t.-  spnns.  the  ni.'iin  an-hes  of  whieh 
fire  .h.s.o-ne.l  without  n.inr..ree,uent.  In  ivfeirneo 
1"  ;'":  '>'"1-""  M..n,ori;,l  l-.ri.l-e.  noted  in  this  tiihle 
:<'i.l  illustnite.l  on  pfiuv  7:.  th.-  ,h-sij,-n  enlls  for  .i 
''■""-"'■  ■"""""'  "'■  "let.-il  reinfoiv.MiH'nt.  not  for  the 
purpose  ,,r  resisting  ■.my  tensih.  stresses  in  the  jireli. 
'"It  nither  to  snpph.ni.'nt  tlie  ,.,nierete  in  r.'sistin.' 
•'"•''••<  --npression.  This  is  ;,  new  prineiph-  in  „reh 
'•"iistrnctioii.  not  pr.nioiisly  use,]. 

mnstnitions  nui\   deseript  ions   of  two  ohl    K,,nuin 

'"••dues     aiv     .-dso     ojven     \\,V    the     p„rp,»s..     of     e;diin- 

■•'""'"'■'"  '"  111-  sup,.riurily  .•,n.l  p.-rnn.n.-.ie,.  ,.f  ma- 
sonry hndnes  over  those  of  .ny  oth.-r  known  tvpe 
'"■  •"■•"'■'•'■•''■  They  h=ne  exisie,l  for  .-."ut nri,.s.  iin-l 
-^H'-'!  !.i  id^vs  sliuuhl  ,.ndnre  after  inetal  hri.luvs  have 
dis:ippcai-e(]. 


^ 
H 


J  l!  'ill 


'    !!. 


M. 


p  li 


V 

nil 


74       coxcRi'Ti:  itk'iiHir.s  .ixn  cn.iT.RT!!. 

Ponte  Rotto,  Rome. 

As  it  stands  to-dsiy.  tliis  old  liridsc  lins  tlirco  stone 
arch  spans,  and  a  suspension  bridj^c,  spanning;  the 
{?ap  where  oflier  arehes  (>ri«rinally  stood.  The  pres- 
ent bridjre  stands  on  the  site  of  tlie  (dd  Tons  Aeniil- 
ins.  Itnilt  H.  (\  17S-142,  Avhieh  was  the  first  stone 
hridfje  over  the  Tiber  at  Koine.  Tlie  tliree  reinain- 
ijijr  arehes  date  fi-om  Julins  TIF.  and  are  richly  orna- 
mented. Two  arehes  were  carried  away  by  a  flood 
in  1508,  and  have  nev<'r  been  replaced.  The  bridfr<' 
H+'cnis  to  be  nnfortunately  located,  as  it  has  been 
carried  away  at  least  fonr  times,  tlie  first  time  in  A. 
T).  2S0.  It  was  erected  by  fains  ^'lavius,  and  is 
probably  tlie  first  appearance  of  the  arch  in  brid«rc 
construction.  Tt  has  semicircular  ar<'hes  and  a 
level  roadway.  The  two  end  arehes  were  shorter 
than  the  three  intermediate  ones.  It  i;.  called  also 
I'ons  Palatiiuis.  Senators'  IJridfre,  and  Pons  Lapi- 
deus.  Th<'  bridjre  is  similar  in  construction  to  the 
other  old  stone  bridjres  of  Kome.  and  is  built  of 
peperino  and  tufa,  faced  Avith  blocks  of  travertine 
anchorecl  into  the  body  of  the  masotiry.  Tt  will  be 
seen  from  the  illustration  that  the  spandrels  ai;d 
parapets  are  liijrhly  ortuunented  with  <'arved  panel 
work  aiul  each  of  the  ])iers  above  the  arches  and 
foundations  an-  ])enetrated  with  snudler  andi  open- 
injrs.  The  panel  work  has  disapi)Pared  from  the  left 
shore  s|)an  and  i)lainly  reveals  the  plan  of  eonstnii-- 
tion.     It  will  be  seen  that   the  arch  rin<r  is  built  of 


'A 


16 


•  lid'cn-iil  iii:it>riiil  .mil  diffcrctilly  laid  than  U\o 
fil!iii<r  :il)nv('  i!.  ;ii)(i  tluif  minuTous  openings  (iccur 
in   till'  l)ackiii«r  wliicli  were  .Imihllfss  used  for  the 

puvposc  of  jiti.-Iioriiitr  tl niiimcntai   fnciuf;  to  the 

ImhIv  nl"  tlic  sf  ciictiin'.  Tf  is  \vell  l<iiowji  that,  in  the 
eoiistnictidii  tpf  l)ri<l^'.'s  iiiid  n«|Ue(lu<ts  huilt  by  the 
TfiiMwMis  mill  utlier-s  in  .ai'ly  times,  a  lart't-  amount  of 
coiiel-t'te  was  used. 


1^  ^ 


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1 

t  i 


\i^l 


Bridge  of  Augustus  at  Rimini. 

The  old  Koman  I)rid<re  erossiiiff  the  River  ]\Iara- 
••liia  at  l{iniini.  is  supposed  to  liave  been  huilt  durin«» 
th.-  iviu-ii  (.r  Kmp.-ror  .\ufrustus.  about  14  A.  D.  It 
has  five  ai-ch  spans,  with  xci-y  heavy  piers.  The  de- 
tails that  still  i-emain  show  that  oriffinally  the 
bridi;.'  Avas  very  ornamental.  There  are  niehes  at 
tlic  pie!-s.  ami  the  heavy  stone  corniee  is  earried 
on  nui.'i. -roils  1. rackets.  The  arehes  are  all  semi- 
'■'"'  ':"■•  <li.'  end  ones  havinj?  a  span  of  2')  feet, 
whih'  till'  three  internie.liate  ones  have  spans  of  28 

lert. 

Henry  Hudson  Memorial  Bridge. 

(K'eiid'oreed  ('onei'ete  Design.) 

It  is  proj.osed  to  erect  on  an  extension  of  River- 
side Drive  ill  the  City  of  Xew  York,  a  Aremorial 
liiidiic  over  Spuyten  Dnyvil  Creek,  to  eommeniorate 
tl'e  cxploialiuns  and  discoveries  of  Ileii.-y  Hudson. 
The  desijrn  aeripted  by  tlie  Municipal  Art  Coiiinus- 


I 
\ 


-i 


y. 

7. 


n 


MICROCOPY    RESOLUTION    TEST   CHART 

(ANSI  and  ISO  TEST  CHART  No.  2) 


1.0 


I.I 


3.2 
3.6 

4.0 


2.5 


12.2 
2.0 

1.8 


1.25 


1.4 


1.6 


^  /APPLIED  IN4/IGE     Inc 

^^.  1653   East   Moin   Street 

r^  Rochester.    Ne«    Vork         U609       USA 

.SS  (716)    482  -  0300  -  Phone 

S^  (716)   288  -  5989  -  Fa« 


n 

t'-- 

I 


!  ; 


Ts       (<)\ch-i:ii-:  liRiiHiiiS  .i\n  cn.rr.NTS. 

si(.ii  of  the  (Mty  of  N'cw  York   is  lUTcwitli  shown. 
I'n'vions  (l«'si'_'ns  showiti«i:  the  priiiciiial  span  fraiu(Ml 
in  steel  Avere  rejected  as  hein^'  inappropriate  for  a 
•jreat    memorial    brid},'*'.     There    Avill    be    one    span 
with  a   elear  len<rtli   of  70:]   feet,  and  seven   other 
semicirenhir  areh   spans  with   elear  lengths  of   lOS 
feet.     The  tolal  lenirth  of  the  strnetnre  will  he  2,S40 
feet.     The  main  aich  span   will  have  a   rise  of  177 
feet,  and  will  contain  a  larfre  amonnt  of  steel,  used, 
not   as  concrete  reinforcement    ordinarily   is.   to   i-e- 
sist  tensih'  stresses,  hut  rather  to  assist  in  resistin'Jf 
the  compressive  stresses  in  the  concrete,  and  there- 
by reduce  the  amount   of  masonry.     The  arch  will 
have  a   crown  thickness  of  IT)   feet.     There  Avill   be 
iwo  decks,  the  upper  one  carryinjr  a  ."0-foot  road- 
way and  two  l.Vfoot  sidewalks,  while  the  lower  deck 
Avill  be  70  feet  in  width,  and  will  carry  four  lines 
of  electric  railway.     It  is  the  intention  to  <nnit  the 
construction  of  the  lower  de(d<  at  the  present  time. 
The  desi«:ii   ])rovides  for  a   clear   headroom   of   18.3 
feet  luider  the  main  andi.     The  nuiin  pieis  will  be 
ISO  feet  in  width.     The  estinuited  cost  is  ^'^.SOO.OOO. 
Tlie     illustration     shows    the     bridge     as     it     Avill 
ai)pear  to  an  observe)'  btoking  out  over  tlie  Hudson 
iriver.  with  the  Palisades  in  the  distance.     The  do- 
sign  Avas  made  by  the  bridge  department  of  the  City 
of  XcAv  York,  at  which   time   ('.   M.  Tngersoll  Avas 
Chief  Engineer.  I..  S.  :Nroisseiff  Engineer  in  Charge. 
Wm.   H.   liurr.   Consulting  Engineer,  and  AYhitney 


/V..//.V  coxcKirrii  arch  BRinci-.s.  79 

Warron.     Architect.     The     ncx^     lonjrcst     iiuisoury 
iirdios  of  tlic  worlil  arc  as  follows: 

Foot, 
span. 

Stono  arch  bridjro  over  Adda  Kivor 230 

Stono  arch  hridirc  at  liuxcniburjr.  (ioniiaiiy 27S 

Stono  arch  hridjjc  at  I'lancn.  Gonnany 20.") 

Concroto  arch  bridjro  at  Oruonwald 230 

Conorote  arch  bridjro  at  AValnut  Lano.  riiiladd- 

phia    233 

r>toin-Toufcn  bridge.  Switzerland 259 

Concrete  arch  bridtre  at  Kocky  River,  Cleveland. 280 
Aulxland.   New  Zealand 320 


Aukland,  New  Zealand,  Bridge. 

A  reinforced  concrete  arch  bridge  is  being  built 
on  the  North  Island,  at  AnUland,  New  Zealand,  with 
a  dear  span  of  320  feet — the  longest  in  existence. 
Several  longer  ones  have  been  i)ro.jected.  one  over 
the  ^Mississippi  l?iver  at  Fort  Snelling.  ]\Iinn.,  with 
two  si)ans  of  3r)0  feet,  but  none  built.  The  Aukla?id 
bridge  has,  besides  the  320-foot  center  span,  two  3.')- 
foot  and  four  70-foot  spans,  with  a  total  length  of 
010  feet.  It  is  40  feet  wide,  and  the  roadway  is  147 
foot  above  the  valley.  The  two  arch  rings  are  hinged 
at  the  springs  and  center.  Tt  was  connuenced  in 
February.  1008.  and  the  contract  calls  for  comple- 
tion in  two  years.  Tt  ad.joins  a  residential  district, 
and  at  one  end  are  the  gi-aves  of  New  Zealand 
pioneers. 


I  :  i 


;     i 


S(»  COSCRIiTE    BNIIXJliS   .IXP   CriAllKTS. 

Monroe  Street  Bridge,  Spokane,  Wash. 

Ill  tilt'  city  (»f  Spokane,  Wash.,  plans  are  prepared 
lor  buildinjjf  a  four-span  c'onerete  bridge  to  carry 
]\ronro('  sIriM't  at  a  lieight  of  140  feet  above  the  S])o- 
i<ane  Kiver.  Tlie  main  areli  lias  a  clear  span  of  281 
feet,  and  is  divided  into  two  ribs.  U)  feet  wide  and 
»i  feet  thick  at  the  crown.  It  will  have  open  span- 
drels and  ovei]ia!i«>ino:  sidewalks,  with  Dutch  towers 
;it  the  ends  for  public  la\atorii's.  The  bridge  will 
replace  the  (»ld  steel  cantilever  built  17  years  ago. 
It  will  have  a  50-foot  loadway  and  two  0-foot  side- 
walks, making  a  total  width  of  71  feet  and 
a  total  length  of  701  feet.  The  main  arch 
will  be  segmental  and  the  remaining  ones  semi- 
circular. The  deck  will  be  carried  on  solid  cross 
spandrel  walls,  20  feet  a[)art.  The  ground  on  the 
north  side  of  the  river  is  naturally  suited  for  an 
arch  bridge,  but  on  the  south  side  the  plan  proposes 
an  abutment  carried  down  to  140  feet  below  street 
level,  consisting  of  four  parallel  walls,  each  4  feet 
in  thickness,  joined  by  numerous  cross  struts  and 
braces.  See  Fig.  Ki.  J.  C.  Ralston.  City  Engineer. 

Rocky  River  Bridge,  Cleveland,  Ohio. 
A  concrete  arch  l)ridge  with  the  longest  masonry 
span  in  America  is  now  being  built  over  Rocky 
River  on  Detroit  avenue,  at  Cleveland,  Ohio.  It  will 
have  a  central  span  of  280  feet  and  five  approach 
spans  of  44  feet  each.  It  will  carry  a  40-foot  road- 
way and  two  sidewalks  8  feet  Avide  each.  The  total 
width  over  r;  lings  will  be  t.O  feet  and  the  total 
length  708  feet.     The  main  span  consists  of  two  sep- 


1  n 


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17.   a: 


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i  a 


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1 


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}  'JS^--r''>£l^y"^f^S.'!'T 


'•^!mt'J9im^^ss.wir:''i^iMj:t 


117 


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III 


fcii  \  \ 


y. 


82 


iWL;. 'tfi 


83 


il 


"•^H^^^^^-Vf^iWr-^'  "'«!^^*F'?f?W!K?^'"J^a>"W:'- 


84 


cosch'i.Tii  liRinci-s  .\\n  cci.iiirts. 


1    I 


!     i 
I.     i 


! 


ai-iilc   arcli    riiu'-s    :s   f,.,'t    wide   ;il    ili(.   crown,   atul 
plaiMul    Iti  feet   apiirt.     On  tlicsf  arclics  tlic  deck   is 
In  1h'  carried  on  cntss-sparidrcl  walls.     The  roadway 
level  is  !M  feel  above  tlie  surface  of  l(»w  water  and 
til"   pavement   will   be   of   brick,   with   two   lines   of 
traek  for  heavy  suburban  ears,     lieneath  the  floor 
ve  to  be  two  subway  chand)ers.  :i  feet  by   11    feet 
/•  the  placitiir  of  pipes  and  wires.     The  main  arch 
ring's  will  contain  no  steel  reinforcement,  as  the  cal- 
eulations  show  that   n(»  tension  can  at  any  time  oc- 
fur  in  any  part  of  the  ani.     The  sidewalks  i)ro.ject 
out  over  the  face  walls  about  five  feet,  and  are  sup- 
ported  on   brackets.     The   entire  strueture   will   b;; 
built  of  concn^te.     Jt  will  be  (piite  similar  to  and  47 
feet  lon«r<  r  than  the  Waliuit  I.ane  Bridfre  at  Phila- 
delj)hia.     The  oidy  lon<rer  uuisotiry  arch  span  in  ex- 
istence is  th(>  one  at    IMfuen.   in   (Jermany.   with  a 
span  of  2!)()  fe.'t.   built  of  hard  siate.     Other  pro- 
jeeted  ioiifr-span   bridfr<'s  are  that   over  the  Xeckar 
River  at  ]\ranheini.  with  a  span    n  '*->et.  and  the 

Hudson  .AFemorial  Uridjre  in  X.  City,  with  a 

span  of  liV.]  feet.  The  Kocky  Kiv.  P.iMdsre  Avas  de- 
sisrned  under  the  direction  of  A.  ]i.  Lea,  (Vmnty 
Engrineer.  hy  A.  :\r.  Fel«,Mte,  Bridjre  Enirineer.  It  is 
under  eonstruetion  by  Schilliufrer  Brothers,  con- 
tractors of  Cliicago.     Wilbur  J.  Watson,  Engineer. 

Walnut  Lane  Bridge,  Philadelphia. 

Walnut  Lane  crosses  the  Wissahickon  valley  on 
a  new  concrete  bridge  at  a  height  of  147  feet  above 
the  river  bed.     At  the  time  of  completion  it  was  the 


ta  ^ 
M    2 


U 


t« 


ft&W^ 


-w^f^n 


f 


8(; 


CO.Vt /«•/; //•    liUllHil.S    .\\n   CUI.rKRTS. 


loiifft'st    concn'tc    iiijisonry    hridjjc,    haviti>»   u    clear 
spiui  of  2'.H  feci.     It  consists  of  two  soparate  an^li 
riii«rs,  IS  feet  wide  at   the  crown,  increasing;  to  21 
fc(-t  (i  inches  at  the  sprinf,'s.     At  the  crown  tlie  two 
ring's   are   separated    by   a    space    of    l(i   feet.      The 
double   rib   consl  ruction    is  siniihir  to   tint   used   in 
the  .stone  arch  bridjre  sit  Luxendjiirp,  (lerniauy,  hav- 
ing'  a    si»an    ol'    27.')    feet.      The    main    arch    is    an 
•ippn.  viniate    ellipse,    has    a    rise    of    7:{    feet,    and 
carries    ]()    cross    walls    which    support    the    tloor 
system.     There  are  also  five  semicircular  approach 
arches  with  clear  spans  of  T),}  feet.     The  bridj?e  con- 
nects Gerniantown  and  IJoxboroujrh.  two  residentinl 
.suburbs  of  Philadelphia.     It  has  a  40-foot  roadway, 
and  two  lO-foot  si(lewalks.     The  entire  structure  is 
solid  concrete,  not  reinforced,  except inj;  in  certain 
minor  details.     TI  -  surface   finish   is  rough,  sinne- 
what  sin-Mar  to  pebble  dash,  but  of  coarser  grain. 
The  exposed  surface  shows  stone  clips  of  not  over 
three-eighths  inch  in  size,  formed  by  washing  before 
the   cement  had    Jiardened.     The    total    length    of 
bridge  over  all  is  58.')  feet,  and  the  cost  $259,000. 
(reorge  S.  AVebster,  Chief  Engineer.  Bureau  of  Sur- 
veys.    II.   ir.   Quimby.    P,ridge   Engineer.     Reilly   & 
Ividdle,  Contractors. 

Connecticut  Avenue  Bridge,  Washington. 

Connecticut  Avenue,  one     f  the  chief  tlummgV 
fares  of  Washington,   is  carried  over  Rock  Creek 
valley  near  its  junction  Avith  the  Potomac  on  a  new 
concrete  arch  bridge,  about  three  miles  from  the 


//: 


87 


,«  »^-^'5»*' 


88 


coxcNini:  hkiihus  .i\n  cii.ii.hTs. 


lii  ■  • 


l'<\  \ 


('Hpitol  l)uil(liii<r.  The  nunhviiy  is  1l'i>  fii-l  jil)(»v<' 
the  vaih'V  Ik'Iow,  iiiid  is  ciirritMl  l>y  live  sriiiirin-ii- 
l;ir  an-lics  of  loO-fuof  spiin.  aiid  two  end  iirrlu's  of 
S2-f()<it  spjMi.  It  has  ;i  .{.Vfont  I'oadway.  and  tun 
Kid. 'Walks  S  feet  wide  carli.  niakitiLT  a  total  widfli  of 
iVJ  I'cct.  a  clear  Iciifjlli  hflwccn  almt iiii-nts  of  l.(»»iS 
ftH't.  and  a  tnfal  Ictifrtli  of  l.:{41  I'fcl  [t  was  .•oiii- 
iiHMiccd  it)  iSSf),  and  ('oiiiplctcd  in  l!M)S.  The  main 
ai'r-hfs  at'!'  Iiinjrclcss  with  no  i-ciid'on-intr.  hut  tin 
spandrel  an-lics  have  steel  reinforcement.  As  the 
bridfje  is  located  in  a  tine  residential  disti'ict,  'U 
aesthetic  appearance  was  a  matter  cd'  consideral»!  • 
importance.  The  face  rinjrs  oi  tlie  aivli.  pii^r  cor- 
ners, mould  in<rs  and  all  trimmiiijxs  lielow  Iheirranit.' 

t'opin<r.  an )ulded  concrete  hlocks.    The  remaininir 

part  of  the  cNposed  concrete  surface  is  hush  ham- 
merpd.  for  the  purpose  (d"  present  injr  a  moie  uniform 
and  pleasiiiff  appearance.  The  cost  (.f  the  falsework 
was  about  !fir)().0()().  hut  on  this  there  was  a  sal\a«,'e 
of  about  $13.(»()().  The  cost  (d"  fraiiiin<r  the  false- 
work was  -t!)  |)er  Hi  .usand  feet  of  lumber.  .Moulded 
cement  blocks  cost  .+  1.')  per  cui)ic  yard.  The  total 
cost  of  the  structure  complete  was  i;^ ■)<>.(><)< ).  equal 
to  $(;;}*)  per  lineal  foot,  or  .tl2.;^(>  per  s<|uare  fo(tt  of 
Hoor  surface.  It  is  built  from  a  modili.-ation  (d'  tlic 
prize  desifrn  submitted  by  the  late  (icor-re  S.  Morri- 
son. The  orijrinal  c(mi|)etitive  desijrns  estimated  1:. 
cost  from  .t-lTO.OOO  to  >:1.1()().()()()  were  published  ii; 
En<?ineerin^  News  Jatniaiy  27.  1S!)S.  j)  xvjis  bull' 
under  the  direction  oi  Col.  dohn  Hiddl,'.  Hntrineer 
Commissioner  of  the  District  of  Cohnnbia.     AV.  J. 


ffi- 


'sir-v^^-'W  ■•'taAi 


8B 


O 
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it 

a 


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90 


coxcRRTE  RRincr.s  .ixn  Cri.lI-RTS. 


I  ; 


i      ! 


l)()n<;liis.  liridii*'  Kii^iiiccr.     K.  1'.  Casey  Coiisiiltiiii? 
An-liitfM't. 

Big  Muddy  River  Bridge,  Illinois. 

Two  tracks  of  the  Illinois  Central  Railroad  are 
carried  over  l>ig  ^Mnddy  Kiver  near  Grand  Tower, 
Illinois,  on  a  new  three-span  concrete  arch  bridge. 
It  was  huil'  in  1003  to  replace  an  old  steel  bridge, 
and  for  this  reason  the  piers  remain  in  their  original 
location.  The  liridge  has  three  clear  openings  of 
140  feet,  and  a  total  length  of  4():{  feet  between  faces 
of  abutments.  It  is  ')2  feet  wide,  contains  12,00!) 
cubic  yards  of  concrete,  and  cost  complete  .tl2-">.000. 
The  arches  are  true  ellipses  with  semi-minor  axes  of 
:U)  feet.  The  old  piers  were  0  to  10  feet  in  thick- 
ness, and  the  new  ones,  which  were  built  around  the 
old  ones,  are  22  feet  thick.  The  main  arches  are 
solid  concrete,  the  only  reinforcing  being  in  the 
spandrel  arches  snpi)orting  the  floor,  and  this  was 
used  for  convenien<'e  in  erection.  As  built,  with 
spandrel  arches  and  oi)enings.  the  cost  was  some- 
what greater  than  if  it  had  been  filled.  The  de- 
signer explains  that  open  spandrels  were  used  for 
the  purpose  of  reducing  tlu^  load  in  the  foundations. 
P.ig  ]Muddy  Uiver  P>ridge  was  designed  by  TI.  W. 
I'arkhurst.  Engineer  for  the  Illinois  Central  Rail- 
road Comi)any. 

Santa  Ana  Bridge,  California. 

This  structure  carries  the  new  line  of  the  San 
Pedro,  Los  Angeles  and  Salt  Lake  Railroad,  over 
Santa  Ana    River,  near  Riverside,  California.     The 


[1    : 
II    ' 


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.ir?aEBs^r'.«  /""if^s^mi 


n 


^- 


»."--:-'"«• 


wm^ 


rL.UX  COXCN/iTIi  ARCH  BRIDGliS. 


93 


bridgrc  has  a  total  length  of  984  feet,  and  the  deck 
is  5.')  feet  above  the  -water.  It  was  l)uilt  during  the 
years  1902  to  1904  under  the  direction  of  Henry 
IIuMgood,  who  was  tlien  Chief  Engineer  for  the 
above  railroad  company.  It  contains  eight  senii- 
circnhir  arches  of  'f^Cy  feet  clear  span,  and  two  end 
spans  of  :i8  feet.  The  piers  are  14  feet  in  thickness, 
making  the  distance  on  centers  of  main  piers  100 
fei't.  It  is  made  of  solid  concrete  without  reinforce- 
ment, contains  12.r)(>0  cubic  yards  of  concrete  and 
cost  .tlS.').:500.  The  thickness  of  arch  at  crown  is  3 
feet  <;  inches,  and  the  width  across  soffit  is  17  feet 
and  0  inches. 

A  leltei'  from  ^Ir.  Tlawgood  to  the  author  in  ref- 
("•cMce  to  tliis  1»i-idge  states  as  follows: — "The  Santa 
Ana  viaduct  has  given  entire  satisfaction  from  an 
o[)crMtiiig  standpoint.  There  has  been  no  cost  for 
maintenance  during  the  five  years  it  has  been  in 
service,  whereas  a  steel  briilge  would  certainly  have 
involved  some  ex[)ense  during  the  same  period.  In 
positions  such  as  the  Santa  Ana  Viaduct  wher" 
liiei-e  is  no  limitation  as  to  headroom,  I  consider  the 
simple  concrete  structure  without  reinforcement  a 
better  structure  than  one  reinforced.  The  greater 
weight  of  concrete  retpiii-ed  forms  a  much  heavier 
nuiss  to  take  up  the  imi)act  of  heavy  high  speed 
(i-ains.  The  absence  of  vibration  is  very  marked. 
It  is  a  tu'i'idlel  condition  to  a  heavy  ai.vil  under  a 
st'-am  hammer — the  heavier  the  anvil,  the  longer  it 
will  last." 


VY  i 


94 


coxcRF.ri:  nh'incEs  .ixn  culverts. 


J 


TABLE  I 


LIST  OF  CONCRETE  BRIDGES 


li'  i   ! 


t  J 


t   ] 


i 


I.(M.ATI()\. 


3 

4 

5 

6 

7 

8 

9 

10 

11 

12 

13| 

14 

1.'^! 

19 
20, 

2]| 
22 
23 
21, 

52l 

2 

28 


Over. 


Hudson  Mem.,  New  York. 

ti  il  tt       tt 

Auckland,  \.  Z '. 


Spuyten  Duyvil. 


Detroit  Avenue,  CleNelaiid  . 

41  H  tt 

Walnut  Lane,  Philadeiiiliia 


Ciruenwald,  Rasaria. 

rirn,  (iennany 

Keinjpton,  (ierniany. 


Kocky  Hiver..  . 

n  tt 

Wissahickon.  .  . 
tt 

Tsar 


Railway  Yards 
Iller  Jtiver 


LaufrMi'h,       "  

Nec'^arhausen,  'Jerniany 

Munderkimjeii,  A\  urteinhurtr.  . 
Connecticut  Ave.,  Wash  imton. 


Neckar .... 
Danube.  .  . . 
Reck  Creek. 


Porfljinil,  IVunsylvania '  Delaware  River  . 


Vauxliall,  London 

'irand  Tower,  Illinois 

In/.i(rliofen,  (Jertnany | 

Edrnondson  Ave.,  Ba!tiin>(re I 


Thames 

Big  Muddy  River; 

D'lniibe 

Gwvniis  River 


7   Rorrodale,  Scotland I  Borrodale  Burn 


1      ^ 

.1 

c 

1 

:    1*703 

177 

2840 

7^108 

1,320 

910 

2  35 
4  70 

:     1280 

80 

708 

5  44 

22 

'     1233 

73 

585 

5l  53 

26.5 

2'230 

42 

720 

1210 
1211 

87 

500 

3  68 
1187 

32 

280 

l|l65 

13.5 

1164 

16.4 

r)ir,o 

75 

1341 

2   82 

41 

■   >   •   ■  < 

5150 

40 

1450 

2120 

1450 

2  30 

1450 

1144.6 

18.5 

3140 

30 

483 

1141 

14 

150 

1139 

44 

542 

3j  60 

30 

542 

1127. C 

22.5 

2  20 

I'l.AlX  C(K\\h'l:H.  .\RCIl  iu<iih;i'.s. 


<j5 


TABLE  I— Continued 


LIST  CF  CONCRETE  BRIDGES 


su 


4;/ 


(50 
fiO 

m 
m 

2.i 
46 
54 


"  I 
147 


94 

94 

147 

147 


('. 
E. 
C. 


C. 


Hcfcn-iice. 

c 

N., 

Ellg.  \ews 

"5 

H.. 

"       Ueronl 

1 
S 

i9;;8 

ti 

1909 
1 <»()<) 

If 

1904 
1905 
1900 


H. 
H. 

II. 
TI. 

II. 

H. 


;i,.SOO,00()     MoisseifT 


.\.,  Nov.    21,  '07 
I   l{.,  Dec.     2S,  '07 


1 
2 

■i 

\  4 


N.,  Jan.     ;il,  '07;  N 


20,S,;i00      loliiate 

2(;2,0()')      AVebster 

"  N.,  Jan.     :}1,  '07j  9 

05,000  I  Munich  N.,  Feb.     2:i,  '05:10 

45,00<i  I X.,  Mar.  1.5.  '00  1 1 

12 

i:i 

14 
15 
10 
17 
IS 
19 
20 
21 
'22 
2;i 
24 


U.8| 
15  8 


40  Sen.    1900  l{.  1! 


52 

120 

V. 

52 

c. 

:n 

05, 

El. 

;m 

65 

;ii 

05 

45, 

E. 

L? 

i9o;i 

1S9;5 

ii9or 


H. 
H. 
H. 


21,000 

I  eibbrami 
21,t2f)  ;  Leibbran.l 
8.50,000     MorrLxon 


\.,  May       2,  '07 
X.,  Mar.    20,  '08 


1908;K.  J{.' 


Bus 


12.5 
00 
•lO 


70' 
70i 


>e^ 


1908  }{.  K.I HiLsh 


1908  1{.  ]{.! 

1899...    .1 
1902  1!.  R.i 
1V95     H. 
1909|    H. 


12..,  JO 

«),0.->0 

]S'5,.X00 


I'.ush 
IMiinie 
Parklmrsf 
Leibbrnmi 


|{.,  -Viifi.  15,  '08 
i{.,  .\up.  15,  '08 
R.,  .\u>;.     15,  '08 

.\.,  Nov.  12,  '(W 
N.,  Sept.  17,  '90 
H.,  June  19,     '09 


lS98iH.  H, 


iO 


Siiiiii.M.p          \.,  Feb.       9,  '99  27 
'28 


Bi;  i 


Ml 


9c       c().\\'h-i:ri:  nuincr.s  .ixn  chahrts. 


TABIE  I— Continued 


LIST  OF  CONCRETE  BRIDGES 


;  I 


I.(X  ATIOV. 


0  er. 


29 

30 

31 

32 

33 

34 

35 

36 

37 1 

38 

39 

40 

41 

42 

43 

44 

45 

46 

47 

48 

49 

50 

51 

52 

53: 

54j 

55 

56 


Sixteenth  St.,  ^^'ashiilKt<)Il I'iiiey  Creok.  . 

Kirchheini,  Wurtembiirj;; Xecktr 

Ilainsburw,  New  Jersey I'.iulins  Kill..  . 


Miltetiburj;,  (leriiiany Main. 


PittsbiiiL    PeiinKvlvaniii Silver  Lake.  . 

Thebes,  Illinoi.s Mis.sissii)i)i.  .  . 

11  11  I  11 

Dainille,  Illinois Vermillinii.  .  . 

Meclianicsville,  New  York .Anthony  Kill 


1  12.-) 

4  >4.(; 
.■  1  JO 

2  KM) 
2112 
2107 
2  102 
1  1 00 

5  SO 
1  l()!i 

11  (•.;. 

1  100 

2  NO 
2  100 


Ininaii,  Havaria Eyach.  ...     ... 

WyotriiiiK  Ave.,  I'tiilailel|>hia '  Fraiikford  Creek. 

Hrookside  Park,  Cleveland \  \\\^  Creek 

Riverside,  California Santa  .\na 


Boulevard,  Philadel[ihia '  Tacony  Creek.  . 

Lonj;  Key,  Florida \tlaiitii' 

Mannheim Neokar 

Larimer  Ave.,  Pittsburg Peechwood  Boul 

Spokane Spokane 


.Mmendares,  Cuba 


1  50 

1  9S 

2  »S 
1  92 
S  ,S(i 

I  2  38 
'  3  80 
180  50 
1  365 
1  300 
1281 
2120 
1100 
190 


I 


39  272 
19  450 
60  i  1100 

:  1100 

17.7,  7.33 

50  ,  t;oo 

40   

50  I 

32.5 

40  I  ;};{() 
31.'   

us'  110 

2.N  I  200 

9  :  125 

43  '■     984 

19   

14  i  350 

25  10500 

115    791 

60   

50   


ii 


PL.ilX  COXCRI-TI-   ARCH  BRIlKlhS. 


97 


TABLE  I     Continued 


LIST  OF  CONCRETE  BRIDGES 


^       ^ 


lit 
,{4 

.■jl 


2S' 


40 

11 

11.- 

•)0 


7( 
70 


:v\ 

90 

;}:; 

•  •  •  • 



N    1' 

.'.) 

Sf 

:v2 

12  7 

12 

17.0 

o.j 

KM) 

••in 

IT) 

;«) 

Par. 

c. 


C. 
V. 

c. 


1006 

IS98 


H. 
H. 


190S  1{.  I{ 


1S99 


H. 


r;i." 

c. 

{'. 

Seiz. 
V. 


•)(),000 
46,600 


101,000 


190.-)  K.  H.  .. 

i9n;^i{.jV. ;; 

1N96j"h." 
I90S|  H. 
190.-,^  H. 
1904  R.  H 

1904  H.  R.  .  . 

1905  H.          100,000 
1904  R.  RJ 


4,2S.-, 
102,000 

18.i,0C0 


Rcferpnrc. 
N-,  Enp;.  N'pws 
R-,    "      Record    1 

e 


Fleischiiin 

J5n)\vn 

Nobel 

Diiar.e 


Lfibbrarid 
Quimby 
Ze.siger 
Hawgood 

Webster 
Cvrter 


R.,Jan. 
X.,  Mar. 
R.,  Aug. 

n    N.,  .Iniv 


'1    14: 


'«:!9      H.    wi.itpd 

I    ,.  lial.-.|(iii 


R.,  May 
'n.,"\ov.' 

R.,  Mar.' 

'N.,'i\ov.' 

X.,'iVb." 
W.,  Feb. 
N.,  Mav 

R.,  Sept. 

R.,  iviar.' 
X.,  Oct. 
Proposed 
Projected 


26,  '07  29 
29,  '00  SO 

15,  '08  31 
32 

25,  '01  33 

34 

35 

6,  '05  36 

37 

20,  '02  38 

'39 

3,  '03  40 

41 

5,  '03  42 
'43 

16,  '99  44 
27,  '09  45 
10,  '0646 

9,  '05  47 

'48 

13,  '0949 
19,  '05  50 

51 

52 

53 


56 


u 


*  !   •< 


I  i 


1  I 

I 


In 


'  ^^n\— . 


->^— H 


-    ~    y    r   Z.    '-  Ji.    -    '-    - 


tr. 


fi 


liH 


w    i^-^|i  H  il-il 


=  it 


-  tf  = 


HI!  \l 


>^— h!" 


—     ,     / 


■•^     —    ^ 


'4L' 


Trn 


P     b 


•y:    v: 


r 


b(.   y: 


V. 


-r'-^---!i 


-^  ~    ■■'^    i- 


T    v. 

C  — 


.r-->-; 


/ 


_    -t-    X     -     —   —    -^ 


»« 


'vi^rf^  r^i'^rtl.  v-4 


^aSTll^eM^^xT 


PART  II. 

Reinforced  Concrete  Arch  Bridges. 

H.'ininr.MMl  ...m.-n-f..  nv.-h  hri,!t;,.s  „s  usuallv  built 
"'■'"  •'  7"'l'i""ti"M  of  ar..|.  .-n..!  1„„„..  nn.l  .'....fnin' 
|"«.st  of  tin.  pn.,M.rti..s  of  l»„th  lyprs.  fl,,.  ;,n.|,  .„• 
"'Hiu  properties  pr,.,lon.i„i,li„j,  a.-eonlitiK  ns  Uwv 
li.Mve  a  lar-e  or  small  rise  i„  proportion  to  tlieiV 
span  Flat  an-hes  aet  n.ore  lik,.  lM.;„ns.  n'-anlless 
ot    tlieory. 

Reinfo.ee,!  ,  oneret..  was  first  eonsiclen.]  n.ereiv 
»  '-Iioap  sul.slif„te  iW  stone.  l,nt  its  own  n.erils 
are  now  reeojrnize.l  and  it  is  use.l  in  a  nuunn-r  ae- 
('(»rding  Mith  its  properties. 

A  principle  of  arehite.-tnral  .lesijrn  .len.ands  that 
■nnatum  of  one  material  l,v  the  nse  of  another 
shall  not  be  ma,le.  ami.  th.-refore.  in  .lesijrnin?  eon- 
^•n'te  bridges,  there  shonhl  be  no  effort  to  in.itate 
stoms  but  to  treat  the  design  simply  and  t^-uth- 
ful  y.  keeping  all  lines  in  han.u,ny  with  the  mate- 
iiiil  used. 

The  e.xtent  to  whieh  eonc-refe  and   reinforeed  eon- 
-n'te  are  now  being  used   in  ,»ref,.renee  to  ston..  or 

ste.!u.a>M)o  jndged  from  tl..  f-aet  that,  during  tin. 
:-'ar  190^,  there  was  at  least  twenty  tin.es  more 
-nient  manufaetured  an.l  sold  than  in  the  e<,rre- 
spombng  period,  ten  years  previ.,us.  As  n.ethods 
"t  design  and  eonstruetion  beeo„K.  -e„erallv  lui 
|lerstood  and  as  workn,..,  beeome  more  aeeusiom,  d 
'-  liandl.ng  conerete.  then'  will  be  a  still  ..reat.-r 
'Hunber   of   bridges    built   of   this    material.      L.... 

99  ' 

SCIENCE  &  ENGINEERING  LIBRARY 


: 


I 


100 


!ve^!;>«i/AM>(i 


REIXFORCED    COSCKIili:    .IKCIl    HKHH.I.S.    101 


spans   oxopedinj;   tin to   four   liundn-.l    f.-.i.    uill 

probably  contimu'  to  b."  framed  in  uM'tal.  hut  thcr;' 
is  reason  to  bcli.v,.  n,,,,  .,11  ,„.,[i„,,,.y  t(.wti  jind 
.•ounty  bridjres  and  tli.-  uui.jority  <d"  r.ilroad  brid«r.'s 
will  be  l)uilt  as  poruiaiu'nt  structures. 

Kcinforcod  concrptc  is  a  jrood  couddnatiou  of 
inatcrials.  Concroto  has  a  hifrh  .'ouip.vssiv.' 
stronRtb.  but  is  Moak  in  t.Mision.  Steel  rods  im- 
iMMldod  in  eonerpto  have  a  hi-rh  tensile  streufrth. 
but  are  weak  in  compression.  The  steel,  therefore, 
sfrenjrthens  the  concrete,  and  the  coiK-refe  stilTerH 
the  .steel,  the  streuffth  of  ..iie  thus  suppleuientinir 
tin;  weakness  of  the  other. 

Since  the   bejrinninj;  of  the   cmnpetitive  i)ractice 
ill   bridge   In  Ildiuir.   many   bridfres   have   been   built 
which   are   deficient    in    both    stren<r1h   and    desi;;ii. 
There   is  no  doubt   that   competition   is  responsibb" 
for  many  economic  features  in  steel  brid^'e  desitrii 
and  has  helped  to  a  prreat  extent  iu  developiufr  ,.,m.- 
nomic  methods.     It  was  found  about  the  year"l!)0(). 
that    steel    bridges    were    being    built    entirely    too 
light  and  competition  was  responsible  f,.r  the  con- 
dition.    Previous  to  that  tinu-.   the    various  bridu'e 
••ompanies  were  accustomed  to  submit   competitive 
plans,  an  1    generally    the    lowest    bid    and    cousc- 
'jiiently  the   weakest   bridge  was   the  e-ie   aecei)ted. 
From   that   date   the    policy    begnn    to   change.    i,n<l 
nistead  of  calling  for  competitive  designs,   a   com- 
iM'tent  engineer  was  employed  to  prepare  plans  and 
co.npejilive  prices  w.-re  then  received  on   his  plans. 
The   policy  of  employing  an   engine<.r  wjiosc   prin- 


0\ 


I 


'♦ 


I 


III 


i  I 


lo: 


iOXCRi-.n:  Hh'inai.s  .ixn  ci  lihnts. 


cipiil  motive  wMs  f.)  protliicc  Jiti  ci'tMinmii'  dt'sipn. 
has  resulted  iti  <i  niiieli  better  ehiss  (if  hriil^es  than 
inider   the   oM   e(Mn|»etitive  s./steiii. 

("uiieicte  liridjr<'s  are  ikw  in  the  same  sta^re  of 
(h'\el(»pmeiit  .IS  were  steel  h'idjres  ten  years  ajfo. 
Many  eojierete  l)riil^'es  have  been  and  <ire  still  be- 
iiijr  built,  which  are  laekiiifr  in  architectural  de- 
sij;n  and  some  are  lackinj;  in  sti'en«rth.  Th«'  prin- 
cipal reason  for  these  defects  is  that  reinforced 
concrete  bridjrcs  are  oblijred  to  compete  with  struc- 
tures of  wood  and  steel.  When  towns  and  other 
nmnicipalities  reali/.<'  tlie  chances  they  are  taking 
in  acceptin<;  competitive  desijrns.  the  method  of 
securin<r  an  aceeptal)le  one  will  then  be  chun'^ed 
and  a  competetit  enj:ineer  will  be  employed  to  pre- 
l)are  the  plans.  Competitive  prices  will  then  be  re- 
ceived on  these  plans,  but  comix-tition  will  cause  no 
red\iction  of  the  cost  by  weakenin<r  any  parts  of 
the  bri(l<;e.  At  the  present  time,  stone  ami  con- 
crete bi-i(l{;es  exist,  havinir  fadoi-s  of  safety  varyinj^ 
fn..ii  three  to  one  hiuidred  and  fifty,  and  there  is. 
therefore,  a  very  evident  need  for  better  and  more 
rational   methods  ol   desi<;n. 

Historical  Outline. 

Since  the  early  ilays  of  stone  bridge  buildinp;. 
rods  and  bands  of  hoop  iron  have  been  used  near 
the  extrados  of  tiie  arch  from  the  piers  anil  abut- 
ments, to  or  slii;litiy  beyond  the  point  of  i-uplure. 
It  was  foinid  when  the  temporary  arch  centers  were 
removed,   thai   the  arcli   settled  at   the  crown   and 


i 


REIM-ORCEI)    COXCRHTI-    ARCJl    HRID(JL 


S.    103 


there 


(I< 


f< 


MTC     WHS     H     K'rid 

..,,...w,,,^,         ,|*'aill.^        IIP 

"P''ii  at  the  oxtrados  linujichcs.  To  prevent  these 
joints  from  opening,  iron  rods  have  lonjj  been  used. 
There  WHS  then  n<.  p-iieij.l  effort  made  to  stren^tlhen 
the  niHs..nry  arch,  except injr  as  stated  above-.     Con- 

erete  an-hes  are  reinfor 1  with  metal  not  only  at 

Hi.'  extrados  from  the  i)iers  to  the  points  of  "rup- 
ture, but  are  also  strcnj,M hened  at  all  places  where 
there  is  any  pc.ssibiljty  of  fusion  in  the  areb  ring, 
.lean  .Monier  first   betran  usin«r  rcinfor;  on"ret(> 

in    fJenuany    in    the    year    ISfiT.    :•  jng   large 

tlower  pots  and  urns  ..f  ccnu>nt  and      uicrete" within 
sinrrl..    lay.T    of    wire    lu'tting    eud)eddcd    therein. 
.Alonu'r  was  a   gardener,  but   he  foresaw  a  success- 
iul    future   for   this  combination,   and   in   the   next 
ten   years    he    built    a    innnber   of   tanks,    bins   and 
other  snudl    structures   of  the   composite   nmterial, 
Hnd  secur.Ml  patents  from  the  Gernuin  Government 
on  his  invention.     Tntrodu.tion  of  this  construction 
m   Ger  .any.  was  slow,  and  it  was  not   until   1804 
that    t,.c    Moiiicr    patents    were    introduced    in   the 
''"it.'.l  States.     This  system  of  reinforced  concrete 
conlained  a   single  layer  of  wire  n.esh  with  wires 
of   the   .same    size    mi     both    directions.      Professor 
:^lelan  realized  the  weakness  of  the  .Monier  svstem 
and  patented  another  and  improv(.,l  method  of  re- 
ii.torcnig  arches,   by   which  curve.l  steel  ribs  wer<> 
placed  Icnglhwise  of  the  arch  and  imbedded  in  the 
coru'rctc  two  ,u-  three  feet  apart.     T      his  first  do- 
s'gns.  curved  1  beams  wer.'  used  ..n.;  ai,     -r  used 
under  his  patents  for  small  spans,   For  Inrgor  .-nans 


.-i*B4_  '..!-4tt;j:\»i--i 


mm 


101 


COXCRBTE    BRinai-.S   AXD   CULVERTS. 


\\\{\\  a  jrrcatt'r  lliickiicss  df  arch  ring,  he  proposed 
a  system  of  li<»:ht  latticed  <rirders  spaced  from  three 
to  five  feet  apart,  which  system  is  still  in  use. 
These  patents  were  introduced  in  the  United  States 
by  TIerr  von  Enii)er<rer  in  the  year  1893.  and  under 
these  patents  many  of  Am(>rica's  best  concrete 
bridjjes  are  built.  In  the  year  1S!)4,  when  American 
eri,t;ineers  beiran  to  seriously  consider  building  and 
replacing  old  l)ridges  in  the  new  type,  it  was  esti- 
mated that  Kurope  had  not  less  than  two  hundred 
of  these  bridges  built  mostly  on  the  Monier  system. 
A  bridge  Avliich  is  believed  to  be  the  tirst  of  rein- 
forced concrete  in  the  United  States,  was  built  in 
(Jolden  Gate  I'ark.  San  Francisco,  in  1S89.  It  has 
a  20-foot  s[)an.  4  feet  o  inches  rise,  and  a  width  of 
{'4  feet.  It  is  an  ornamental  bridge  with  curved 
wing  walls  built  with  imitation  rough  stone  tinish. 
A  second  one  in  the  same  park  and  of  similar  de- 
sign was  built  in  ISHU  In  U^95  a  70-foot  span  arch 
was  built  by  Ilerr  von  Emperger,  carrying  a  drive- 
w;iy  over  Park  Aveinie  in  Eden  Park,  Cincinnati. 
Tlie  bridge  is  located  in  the  i)ark  at  a  place  nuich 
I'rtMjui'nted.  and  an  effort  was  made  to  make  it  both 
sli'ong  and  beautiful.  The  balustrade  is  highly  or- 
nameiilal  and  llie  spandrel  ualls  are  decorated  with 
panels.  The  iiitrados  of  the  arch  is  much  flatter 
tlian  app<'ars  neces.-ary  and  certainly  a  greater  rise 
would  have  presented  a  more  pleasing  effect. 

During  the  first  ten  years  after  the  introduction 
of  the  Mclan  patents  in  the  United  States,  there 
were  not   more  than  a  hundred  reinforced  concrete 


REIX  FORCED   COX  CRETE   ARCH   BRIDGES.    105 

bridges  built.  Tho  fact  that  a  nion-  gcuTal  intro- 
duction of  this  system  was  not  nuule,  was  probably 
due  to  the  lack  of  more  definite  kuowledjje  anil 
data  in  reference  to  the  action  and  behavior  of  this 
construction  und(>r  live  loads.  European  en,irineers 
were  likewise  embarrassed  by  lack  of  knowledjre, 
so  much  so.  that  durinir  the  years  1890  to  181)5,  tlie 
Austrian  Governnu'iit  undertook  extensive  experi- 
ments on  full-sized  concrete  ar-dies.  The  result  of 
these  experiments  was  entirely  satisfactory,  and 
complete  reports  of  the  investigations  were  pub- 
lished in  many  of  tiie  engineering  journals  of  Amer- 
ica and  Europe.  From  the  completion  of  these  ex- 
perinuMits  in  180r,  to  the  present  time,  the  building 
ol  bridges  in  concrete  an.l  reinforced  concrete  has 
been  on  the  increase,  and  there  ar<.  now  more  than 
a^  thousand  of  these  bridges  in  the  I'nited  States. 
Previous  to  these  experiments,  no  satisfactory 
progress  was  made  eitlu-r  here  or  abroad. 

At  first  it  was  customary  to  use  reinforcing  steel 
id  the  arch  ring  only,  hut  later  structures  and  nu^st 
ol  those  now  being  huilt  have  metal  reinforcenuMit 
throughout.  .Alasonry  bridges  and  Imildings  are  still 
••xisting  that  have  stood  for  many  cnturi.'s.  while 
steel  bridges  built  less  than  forty  y.-ars  ago,  have 
iilready  worn  or  rusted  out  and  have  been  replaced. 
Two  of  these  bridges  have  already  been  illustrated 
in  Part  I  of  this  book,  and  there  are  positive  rec- 
ords of  many  others  .,uite  as  ancient  which  are  .still 
1.1  existence.  Pont  dn  (Jard,  an  old  Koman  a.pie- 
duet  bringing  water  to  the  city  of  \imes,  France 


IOC 


COXCRETr.    BRIDGVS   AXD   Cril'ERTS. 


I; 


if 


is  sn[)posed  to  luivo  boon  built  about  tbo  time  of 
Augustus  in  tho  yoar  19  B.  C.  Tlie  Acjuoduet  of 
Vojus.  consisting?  of  a  series  of  hi«;h  arches,  and 
tlie  dome  of  the  rantlioon  at  Rome,  \vith  «'i  s[)an  of 
140  foot,  are  at  b'ast  1,800  years  ohl  and  all  of 
these  structures  are  oven  now  in  a  fairly  good  con- 
dition. Those  and  many  others  (juite  as  old  are 
built  of  coarse  concrete  masonry. 

Several  American  railroad  companies,  after  re- 
peatedly renewing  their  metal  b"idgos  to  support 
increased  loads  and  rolling  stociv,  have  at  last  re- 
sorted to  building  their  bridges  in  masonry,  know- 
ing that  when  properly  built,  they  will  remain  as 
pcrnuuient  struclures  for  centuries. 

Advantages  of  Reinforced  Concrete. 

The  general  advantages  of  masonry  as  compared 
to  steel  framing  have  already  boon  referred  to  on 
page  1.  These  advantages  r(>ferred  particularly 
to  plain  concrete  rather  than  to  reinforced  con- 
crete bridges.  It  was  stated  there,  that  arch  bridges 
(•f  solid  concrete  v.ore  superior  to  all  others,  and 
particularly  superior  to  arches  wlioi'o  tension  oc- 
curs in  any  part  of  the  arch  ring.  In  pointing  out 
the  commendable  tjualities  of  solid  concrete,  it  is 
not  intended  to  deny  tho  nu'rits  of  i-einforcod  con- 
crete. On  tlie  other  hand,  reiid'orced  concrete 
arches  have  sonu'  decided  advantages  over  solid 
concrete.  Some  of  these  advantages  are  as  follows: 
(1)  Working  units  for  reinforcid  coticrete  nmy  be 
higher  than  for  i)lain  concrete. 


h'f'.ixioh'cr.n  C(K\-CRi:ii-:  akcii  uRinaiis.  107 


CV)  Ilijjlicr  units  pruiliicc  a  lliinnor  arch  riii<»,  and 
conscMniontly  less  dead  load  and  lighter  al)ut- 
nienls. 

('■V)  Fhit  arches  may  be  safely  used,  which  would 
be  impossible  in  solid  concrete. 

(4)  l>ecause  of  their  lighter  weight,  it  is  practica- 
ble to  bnild  si)ans  of  nuich  greater  length. 

(:"))  All  cracks  of  every  description  can  be  avoided 
in  reinforced  concrete  arches. 

(T))   They  have  the  strength  of  steel  with  the  solid- 
ity and  substantial  appearance  oi  stone. 
Bridges    of   both    plain    and    reinforced    concrete 

have  also  the  following  merits: — 

(1,>  They  have  no  noise  or  vibration  and  are  not 
only  cheaper  l)nt  more  duralde  than  stone. 

(2)  Concrete    bridges   with  solid   decks   permit  the 

use  of  ordinary  ties  for  railroad  tracks,  which 
caiHiot  be  used  on  steel  ])ridges  with  open 
decks. 

(3)  T'.ie  tloors  of  concrete  street  bridges  over  rail- 

road tracks  are  not  danuiged  by  the  action 
of  gas  and  fumes  from  locomotives,  as  is  the 
framing  of  these  I)ridges  when  l)uilt  in  steel. 

(4)  Concrete  bridges  reciuire  but  very  little  skilled 

labor. 
(.'>)  A  concrete  arch  bridge  so  designed  that  ten- 
sion cannot  occur  at  any  time  or  under  any 
condition  of  loading,  is  the  most  permanent 
bridge  of  all.  If  no  tension  occurs,  eraek.s 
will  not  form  to  permit  moisture  to  reach 
and  corrode  the  reinforcing  steel,  and  when 


t ,     V 


J 


1     M 


108 


COXCRETP.    liRlDGIiS   .1X1)   CILVERTS. 


tlu;  iiictiil  is  perinaneiitly  protected  and 
sccMiro  rroin  the  atmosphere  and  moisture,  it 
sliould  endure  for  eenturies. 
Deck  l)nd(rcs  are  in  nearly  all  cases  preferable  to 
those  where  the  travel  is  carried  between  lines  of 
side  trnssiii<^  and  l)eneath  systems  of  overhead  brac- 
ing- ^iich  truss  and  braeinj,'  systems  are  a  danger 
anil  menace  to  travel,  particularly  on  crowded  thor- 
(Mijxliriii-es.  iiiid  obstruct  the  space  required  for 
vehicles.  Trussing'  and  bracing  are  also  an  ob- 
struction to  oI)servati()n  and  the  clearance  retpiired 
throu«,'h  the  bridge  revents  the  use  of  lateral  brac- 
ing necessary  to  sti.Ten  the  frame.  Concrete  arch 
bridges,  when  deck  structures,  are  free  from  the 
disadvantages  mentioned  above.  Through  bridges 
should  never  under  any  condition  be  used  for  im- 
portant locations  uidess  the  underneath  clearance 
or  structural  re(|uirements  positively  prohibit  the 
use  of  a  diH'k  bridge. 

For  all  (U-dinary  locations  and  length  of  span, 
there  appears,  therefore,  to  be  no  good  or  sufificient 
reason  for  l»uilding  unsightly  frame  structures 
when  more  permanent  and  artistic  ones  can  be  made 
at  the  same  cost. 

Adhesion  and  Bond. 

Kick  cement  concrete  in  which  iron  or  steel  ig 
embedded  has  an  adhesion  thereto  of  from  500  to 
fiOO  pounds  per  s(juare  inch  of  exposed  surface.  Ad- 
hesion of  concrete  to  metal  occurs  only  when  the 
metal  is  thoroughly  embedded  and  the  concrete  has 


A'FJxrokCE/)  coxch'inii  arch  bridgi-.s. 


109 


opportunity  to  surnmnd  and   grip   H,,.   h^rs.      If  a 
metal    bar    is    jWaccd    sinii>ly    in    contact    with    soft 
concrete  there  \vill  he  but  litth'  adhesion.     For  the 
purpose    of   illustration,    if  steel    plates   are    placed 
on  edge  and  concrete  tilled  in  between,  but  not  un- 
der or  abov.'  then.,  after  the  <-on.-rete  has  hardened 
It    \vdl    be   a    comparatively    easy    matter   to   h.osen 
the  concrete  and   break  the  adhesion.     This  weak- 
ness is  due   lo  the  fact  that  the  concrete  is  simply 
in  contact  with  the  metal  but  does  not  j,'rip  or  sur- 
round   it.      In   contrast   to   this  condition,   if  a   bar 
be  thoroughly  embedded  and  surrounded  with  rich 
eoncr;-!.'.  it  will  adhere  so  securely  to  the  rod    that 
a  pull  of  from  r,00  to  GOO  pounds  for  every  square 
ineh   in   contact   will   be   recpiired   to   extricate   the 
rod    from    its   bed.      In    order   to   develop   the   full 
strength   of  the    rod   u])   to   its   clastic   limit     it    is 
necessary  that   the   end)edded   length   must  at  least 
e((ual  twenty  to  twenty-five  times  the  dianu^ter  of 
the  rod.     This  is  on  the  assumption  of  perfect  ad- 
hesion  between   the  metal   am",  concrete.     The  mix- 
lure  as  ordinarily  used,  instead  of  fine  mortar,  con- 
tains   more  or  less  voids,  which  may  be  considered 
e(pial  to  50%.  of  the  entire  surface  in  contact.     To 
allow   for   watersoaking,   a    still    furtiier    reduction 
of  r.0%   must  b<-  made.     In  ordinary  work  as  found 
m  actual  structures,  the  adhesion  between  the  con- 
crete and   metal,  instead   of  l)eing  fn.m  .lOO  to  COO 
pound.s   j.cr  scpiare   inch,   as   for  fine   test   .samples, 
would,   therefore,    not     exceed     from     125     to     150 
pounds   i.er   square    inch.      IJy    using   a    factor   of 


i 


I 


i 


1    .1 


i  i 


110 


C(>\ci\'i:ii:  i!h'iiK.i:s  .ixn  cci.rnRTS. 


siifcty  ot  five  ;i  workiiif?  adhesive  unit  will  not  ox- 
ciM'd  from  -M)  to  40  pounds  per  scjuarc  ineh  of  sur- 
face ii<  eontact.  The  letigth.  therefore,  that  rods 
must  l)e  eniheilded  in  ordinary  eonerete  to  develop 
their  fidl  slrenglli  up  to  the  elastic  limit  is  about 
four  times  t  w  i-nty-nve.  or  one  hundred  tinu's  the 
diam<>ler  of  the  rod. 

It   has   been    positively   prove'i    by    numerous    ex- 
periments  that     concrete     adheres     as     securely    to 
Knu)oth    rods   as   it   d(;es   to    rou»rh   ones.      Fretiuent 
and   conliiHied   shocks    and     vil)i',itions  tetul   to   de- 
stroy the  union  between  the  two  nuiterials,  and  ex- 
perinu'uts  show  that  contiimous  watersoakinj?  from 
six  to  twelve  months  reduces  the  adhesion  by  about 
lOO'/f.     P(H)r  woiknuinship  in  placing  and  ranuning 
file  concrete  is  also  iti'obable  aiul  for  these  reasons, 
it    is    desirabli'    to    use    reinforcing    rods    that    are 
roughened  or  twisted,  so  the  bar  it. ay  have  a  direct 
mechanical   grip  on  the  conen'te  in  addition  to  its 
adhesion.      ^Vhen    this    roughening    of    the    bars    is 
secured     wiliiout     decreasing     llieir     cross-sectional 
area    the  entire  area   of  the   bar  is   then  available 
for  tension  and   no  strength  is  lost   by  the  expedi- 
ent.     Tioughening    the    bars    can.    therefore,    do    no 
harm  and  it  may  be  a  source  of  extra  strength.    As- 
suming that  the  rough  rods  cost   more  than  plain 
ones,  the  consideration  in  making  a  choice  between 
the   two,   is  simply   whether  the  extra   expense   for 
rough  rods  is  warranted  by  llic  additional  slrength 
that  they  may  give.     While  watersoaking  decreases 
the  ailhesioii  between  the  two  materials,  the  upper 


^f 


RlilX FORCED   COXCRETIi   ARCH   BRIDGES.    Ill 

concrete  surfaces  are  usually  waterproofed,  and 
the  prohahility  is,  that  instead  of  weakeninj?  from 
watersoaking,  the  strength  of  the  concrete  and  its 
adhesion  to  the  steel  will  increase.  The  conclusion, 
however,  is  that  rough  rods  are  preferable.  They 
<'ost  but  little  more,  ean  do  no  harm  and  may  be  a 
Ix'iiefit. 

Metal  Reinforcement. 

Reinforcing   steel    in    concrete    bridges    is    intro- 
duced for  any  or  all  of  the  following  reasons:— 
(1.)   To   resi.st   tensile   stres.ses  due   to   bending   mo- 
ments, 

(2)  To   preve.      cracks   oecurring   fnMii    change   of 

temperature. 

(3)  To  form  a  temporary  working  |)latforin  at  the 

roadway  level. 

There  is  no  sufficient  reason  from  a  scientific 
standpoint  for  the  use  of  high  tension  bars  or 
rods  for  concrete  reinforcement.  After  years  of 
investigation  and  experiment,  brittle  metal  was  dis- 
carded for  structural  use  and  the  only  reason  for 
a  return  to  the  use  of  high  tension  bars  now.  is  a 
commercial  one  and  not  scientific.  It  is  well  known 
that  in  r(!-rolling  bars  to  produce  surface  roughen- 
ing, the  tensile  .strength  of  the  metal  is  increased 
Instead  of  admitting  the  inferior  (lua'.ity  of  their 
products,  interested  parties  have  endeavored  to  ex- 
plain that  this  increase  in  tensile  strength,  and  cor- 
responding decrease  in  ductility  is  a  benefit. 

^Medann    steel    with    an    elastic   limit   of  32.000 
pounds  per  s(piare  inch,  or  soft  steel  with  a  corre- 


i 


!f 


112 


COXCIdim    HHlDGliS  AS  I)   CriA-URTS. 


I  i 


I   •; 


spondinf?  claslic  liinit  of  2.S.(M)()  [xmnds,  are  the 
pnipcr  fi;ra(K'S  of  metal  for  all  ordinary  eoiierete 
reinforeeineiit.  These  may  safely  be  stressed  up 
to  half  their  clastic  liinit  under  workinj^  loads.  If, 
for  any  snlTicient  reason  a  hif?h  tension  metal  is 
desirable,  then  some  ^rade  of  wire  is  preferable  to 
bars.  It  is  dii'fii-ult.  however,  to  secure  f,'ood  con- 
tact between  wire  mesh  and  concrete,  for  the  small 
openinj,'s  in  the  mesh  nuike  it  difficult  to  tamp  the 
two  nuiterials  well  together.  If  a  mesh  must  bo 
used,  then  a  large  mesh  is  preferable  to  a  snudler 
one.  In  nearly  all  positions,  whether  tensile  stresses 
are  liable  to  occur  or  not,  the  presence  of  metal 
in  concrete  will  add  to  its  strength  and  perma- 
nence. Only  in  such  places  wlicre  there  is  insuffi- 
cient space  for  its  insertion,  will  it  be  a  detriment. 
The  rule  generally  is  "when  in  doubt,  use  rein- 
forcement ". 

The  old  Monier  system  of  arch  reinforcement, 
consisting  of  a  single  layer  of  wire  mesh  with  wires 
of  the  same  size  in  each  direction,  is  evidently 
wrong  in  princii)le.  The  amount  of  metal  required 
crosswise  and  longitudinally  of  the  arch  is  not  nec- 
essarily the  same,  for  the  area  in  each  case  must 
be  suited  to  its  need.  For  resisting  bending  mo- 
ments in  the  arch  ring,  when  the  line  of  pressure 
falls  outside  of  the  middle  third,  the  size  of  rods 
will  depend  on  the  magnitude  of  the  bending  mo- 
ments. 

It  was  customary  at  first  to  reinforce  only  the 
arcli  ring,  but  now  all  parts  of  reinforced  concrete 


REIXFORCE!)   COXCRETli   ARCH    BRIDGES.    113 

bridnrcs.  oxeeptinor  perhaps  the  halnstrade  and  othor 
orna mental   features,  are  provided   with   metal   for 
the  purpose  of  hotter  uniting  the  whole  into  a  solid 
monolith.      It    is    partieularly    desirable    that    rein- 
foreement  be  placed  at  all  points  where  loeal  loads 
are    liable     under    any     circumstances    to    produce 
bending  or   tension.     Where   cross   spandrel    walls 
bear   upon   the   arch   -in-    these   walls   should   not 
only  be  well  anchored  to  the  arch,  but  ad.litional 
metal  may  be  required  beneath  these  concentrated 
loads.      The    best   practice   at   the   present    time   in 
reinforcing  concrete  arch  rings  is  to  use  two  com- 
I'lcte  systems,  one  at  the  extrados  and   the   other 
at  the  intrados  of  the  arch.     Some  designers  prefer 
to  reinforce  the  extrados  only  from  the  sprin-s  to 
or  a   little  beyond  the  point  of  rupture,   ondttin.^ 
the  metal  at  the  extrados  crown.     The  saving  by 
this  omission  is  not  great  and  generally  is  not  suffi- 
cient to  warrant  it. 

At  all  points  where  light  walls  or  sections  join 
to    heavier    concrete    masses,    heavy    reinforcement 
should   be   used.     In  setting  and   drving.   concrete 
acts  much  in  the  same  way  as  cast  iron,  and  unless 
ttie  light  sections  are  well  tied  to  the  heavier  ones 
cracks   at   the   junction    will   occur.      This   is    illus 
trated  where  ring  walls  join  to  the  abutments      If 
lor  any  reason,   it   is  impracticable  to  anchor  the 
wing  walls  to  the  abutment  face,  it  is  then  i)refer- 
able  to  leave  an  open  joint,  for  otherwise  an  irreg- 
ular crack  will  occur,  showing  weakness  either  in 
the  design   or  in  the  construction. 


1 1 

1   ( 

|!i  ! 


1 

i 


i 


114        COXCh'Lli:    liRllHil.S   ASn   Cn.VLRTS. 

As  llic  iiliioiint  ul"  iidlifsioii  brtwct'il  slci  ..  .;!  coii- 
crt'tr  (IfpciKls  directly  u|)(ni  tlu'  amount  of  steel 
surface  ill  contact  with  the  concrete,  it  is  prefer- 
able for  securiii<,'  the  "greatest  bond,  to  use  a  larj^er 
iiundxr  of  small  bars  rather  than  a  snuiller  iRUuber 
o^  lar^'cr  ones.  It  is  desirable  also  to  have  tho 
cracks  in  the  concrete  as  small  as  |)ossible,  so  water 
will  not  Ciller  the  cracks  and  corrode  the  metal. 
I'ljon  this  feature  the  duration  of  a  concrete  struc- 
ture depends.  11  water  is  allowed  to  soak  into  the 
cratdis  and  corrode  the  reinforciiij?  metal,  it  will 
then  be  only  a  few  yejirs  \uitil  the  streiifrth  of  the 
member  will  be  destroyed  by  rust.  It  is  necessary, 
therefore,  that  sutTicient  reinforeiuf;  metal  bo  used 
in  order  that  cracks  will  not  be  excessive.  Several 
leadinj;  desi<rncr«  of  reinforced  coiicn^te  are  now 
specifyin<r  that  tension  in  the  concrete  shall  be 
consi(len>d.  and  cno:i{rh  metal  used  so  the  tension 
in  the  concrete  will  not  exceed  a  safe  unit,  which 
IS  usually  placed  at  ai)out  .")()  pounds  per  scpiare 
inch  on  the  cross-sectional  area  of  the  concrete  in 
tension.  The  object  in  this  is  to  prevent  eraeks 
from  formiii<r  and  to  c^xclude  all  moisture  from  the 
metal.  This  is  doubtless  the  ideal  condition,  for 
when  |ierfectly  cm])edded  and  protected  from  mois- 
ture, steel  is  known  to  be  indefinitely  preserved. 
When  insufKcient  steel  is  used,  large  cracks  will 
form  on  the  tension  side  and  the  bridge  is  then 
no  tiiorc  a  }>rrni;;.u'nt  one  than  an  ordinary  steel 
bridge,  or  not  even  as  permanent.  "When  a  steel 
bridge  is  exposed  to  moist ui'c  *he  steel  can  be  ex- 


RLIM-OKCEI)   cose  KE  IE    .IRiJll    OKI  DUES.    M'o 

Jiiiiiiicd  iiiKi   pjiiiitcd.  wlirrt'iis  in  ji   n-iiifoivcd   con- 

cn-tc  l»ri(lK'(\  the  sti-d  is  concealed  fi i  view,  ciin- 

Mot  he  inspected,  nnd  its  collapse  is  the  tirst  warn- 
111^'  friv  II  tlial  I'le  nielal  reinforeejuent  has  been 
<lestroyed.  The  best  results  are.  therefore,  secured 
i>.v  allowinjr  no  cracks  whatever,  hut  if  cracks  must 
form,  lo  have  these  cracks  so  snudl  that  water  can- 
not enter  ihem.  It  is  better  to  have  a  larjre  num- 
!m'1-  <»f  very  small  cracks  than  a  suuiil  nuiubcr  of 
lar<?e  ones. 

'^   '•<'M>iire nf   upon  which  the  streuKtli  of  rein- 
forced concrete  directly  depends,   is  the  amount   of 
.'ontact     between     the     two     composing     materials. 
Every  elfort   should   be   made   to   have   this  contact 
as  perfect   and   complete  as   possible.     In   decidiiij,' 
upon  a   workinj-:   unit    for  adhesion   of  concrete   lo 
steel,    it    is    customary   to    consider   that    imperfect 
workmanship  in  ordinary  structures  will  cause  only 
•iliout   one-half  of  the  exposed   metal  surface  to   be 
actually   <,'rippcd   by   the  cement.      If  a    hijjhcr  de- 
iTi<'('  of  workmanship  l)e  secured,  then  the  stren«,'tli 
of  th     structure  will   be  increased  acc()rdin«,'ly.     It 
is    (•■iisidcred    that    walersoaking   still    further    de- 
creases the  adhesion  by  another  lOO/r.     Therefore, 
if  perfect  adhesion  on  rich  samples  between  the  two 
materials    is    from    r)00   to    bOO   pounds    per   s(|uare 
iiieh.  the  ultimate  adhesion  in  actual  structures  can- 
not b.    taken  greater  than  fnun  12.")  to  150  pounds 
!><'r  sriuare  iiich.  To  develop  the  full  tensile  strength 
of  bars  endx'dded  in  concrete,  it  is  easy,  therefore. 
^  -nmpute  the  length  that  these  bars  must  be  em- 


ifl 


il 


116        COSCR^.Til   BRIDCr.S   .IXf)   Hf.rERTS 

h'Mldcd.  I'siiij;  iiti  iillimalt'  ii«lln'si\f'  unit  for  ordi- 
nary stnu'lurcs  of  !.')(>  |)oinids  per  sfiiunv  inch,  one 
inch  sijuiirc  bars  '.vonld  he  ^'ripped  to  the  extent 
of  <ino  j>..nn<ls  per  lineal  inch  of  bar.  Therefore,  to 
s'cnre  tlie  fnll  elastic  slren>;t!i  of  the  har  up  to 
•{2.n(K».  the  rod  must  he  enihedded  a  nuniher  of 
inches.  (Mpial  to  :{2.(M»()  divided  by  (i.OOO.  or  .').{ 
inches.  ^Vhere  arch  riiifjs  join  fo  piers  and  abut- 
ments, it  is  customary  to  run  the  reinforcini?  steel 
v.-eli  into  the  piers  t(»  deveb»p  the  fidl  stronprth  of 
the  metal. 

Kxperimeuts  show  that  ailhesion  to  steel  is  much 
•rreater  before  the  steel  is  pauited  than  afterward. 
A  sli<,dit  c(»atinjr  of  rust  has  been  foinid  to  add  to. 
rather  than  to  (h'trjK  t  from,  tlu-  adhesive  stren<ith. 
T..oose  scales  or  Hakes  of  rust  must  not  bo  permit- 
ted, but  a  slijrht  rustinfr  is  no  disadvantage.  Kx- 
perimeuts have  been  made  on  vusted  steel  imbedded 
in  ricii  cement,  and  after  a  period  of  several  months 
whvn  the  steel  Avas  renu)ved  and  the  cement  broken 
away,  it  was  found  that  the  steel  ai»|)eared  clean 
and  free  from  even  tlie  slij,'ht  rusting  that  existed 
when  it  was  first  imbedded. 

Lij^ht  reinforcing  frames  are  freciuently  >ised  in 
the  spiindrels  of  reinforced  concrete  bridges,  not 
only  to  strengthen  tlie  concrete,  but  also  to  provide 
a  temporary  working  platform  at  the  roadway 
level.  This  plan  is  illustrated  by  the  Illinois  Cen- 
tral Railroad  Company's  bridge  over  liig  ^Fuddy 
River  near  Grand  Tower.  Illinois.  Bridges  built 
by  Ilerr  AVunsch  in  CJcrmany  were  mostly  of  this 


Rf.lXrORCED   COXCRETE    ARCH    BRIDGES.    117 

type.  The  metal  in  sueh  eases  must  have  sufficient 
slren^'th  to  act  as  eompressive  members.  In  the 
fiij?  ^UuUy  River  hridfre,  the  et.^rineer  used  old 
rails  for  the  spandrel  frames,  and  when  completed 
these  were  eneased  by  the  eonerete  spandrel  col- 
umns. 

Reinforcing  Systems. 

The  principal  reason  for  the  existenee  of  the 
many  patented  systems  for  eonerete  reinforcement 
IS  the  patent  royalty  secured  therefrom.  There  are 
ft  few  essential  requirements,  and  where  these  are 
I'ulfilled.  the  reinforcement  is  satisfactory.  Chief 
among  these  refjuirements  are: 

(1)  The  metal  shall  be  rough  or  have  a  mechanieal 

union  with  the  concrete, 

(2)  Reinforced  beams  shall  have  stirrups  for  trans- 

mitting shear  components  from  the  main  ten- 
sion members  into  the  web  of  the  beam. 
In  connection  M'ith  the  latter  requirement,  it  is 
preferable  that  the  stirrups  be  rigidly  connected 
to  the  tension  member,  in  order  to  secure  a  positive 
transmittal  of  the  shear  components. 

The  various  reinforcing  systems  may  be  roughlv 
classified  under  two  headings. 
(1  »   Slab  Iieinforcement. 
(2)  Beam  Reinforcement. 

Tnder  the  first  heading  are  included  the  various 
kinds  of  expanded  metal.  Light  rods  are  suitable 
for  slabs,  as  are  also  twisted  bars  and  j^lain  fiats 
with  rivet  heads  thereon.  For  beam  reinforce- 
ment,   the    opportunity    for    patented    systems    is 


3^ 


^ 


118        COXCRETE    BRIDGES   AXD   CVLJ-ERTS. 

greator,  niul  a  large  iiumk'r  aro  now  on  the  mar- 
ket.   Among  these  may  be  mentioned  Twisted  ro;  > 
Corrugated  Itars.  Diamond  l)ars.  Tliaeher  ban    Ciii) 
bars.  Twi.sted  Lug  l»ars,  ete.     All  of  these  ar    r  ,ds 
and  i)ars  without  provision  for  stirrup  eonno  tuv-. 
Tri   addition   to   these,   there   is   quite   a   varietj'   of 
patented    bars   on   the   market,   either   in   the    form 
of  truss  frames  or  with  stirrup  conneetions.     Tn  this 
latter  class  may  be  placed  the  Kahn  bar,  the  Cum- 
mings  Girder  Frame,  the  Unit  Reinforcing  Frame, 
the  Luten  Truss,  the  :\Ionolith  Frame,  the  General 
Fireprooling  Company's  Girder  Frame  and  others. 
P'or   slab   reinforcement,   a   coarse   wii-e   with    its 
high     tensile      strength     and     corresponding     high 
elastic  limit,  is  economical.     It  does  not   have  the 
disadvantage  of  high  tension   bars,  for  while  bars 
are  brittle  and  lack  ductility,  wire  is  elastic   and 
has  always  been  and  probably  will  continue  to  be 
a  desirable  tensile  metal.     It  bends  easily,  will  not 
crack  in   handling  and  gives  a  large  external  con- 
tact area  in  proportion  to  its  section.  Certain  kinds 
of   wire    mesh   have   the    principal    strands    in    one 
direction,  united  by  a  lighter  weave  at  right  angles 
to  tliein.     This  type  of  wire  mesh  is  made  with  the 
principal  wires  in  various  sizes  and  is  well  suited 
for   reinfoi-cing   bridge    floors.      Where   floor   panels 
are  sijuare   and   floor  beams   in   both   directions,   it 
is  then  economical  to  use  a  wire  mesh  with  wires 
of  the  same  size   in   each   direction.      Most   of  the 
various  expanded   metal   systems,   while   they   have 
a  lower  tensile  strength,  have  sufificient  stiffness  to 


RiifXroRCf.n    COXCRhlE    .}RC/f    BRinCES.    119 

support  their  own  weight  .luring  constructicn,  and 
i«n"  rougJior  Hn<l  have  a  gn-at.'r  ineehanieal  bond 
than  win".  An  excelh-nt  examph'.  showing  the  vari- 
ous methods  oC  reiuforeenient  for  eouerete  hrid-'es 
IS  a  nhhed  design,  for  (Jraud  Avenu.'  Viaduet'in 
Ahhvaukee.  shown  in  Kigun-  27  and  more  fullv  de- 
s.-nbed  iu  the  Engineering  News,  Februarv  14 
IftOT.  •         ' 

As   the   shearing  stress    in   curved   areh   slabs    is 
qnite   small   there   is    but    little    need    for   metal    in 
the   web.      The  .Alelan   system   has   continuous  lines 
of   double   angle   bars  at   the   extra.los  and   the  in- 
Irados  of  the  arch,  connected  by  light  lattice  work 
;nid  these  are  manufactured  complete  in  the  struc- 
tural shop  and  shipped  to  th<'  l)ri<lge  site  ready  for 
••iretion.      These    frames   are    l)locke,.   up    vertically 
oil   th.>   arch   centers   from   three   to   five   fe.>t   apart 
••••osswise  of  the  bri.lge.  an<l  they  are  connected  at 
'■nervals  with  bars  ..r  franu-s  which  take  the  place 
"I   .'xpansu.n  ro,ls.     Tl„.s..  shop-riveted  frames  con- 
sulerably   snnplify   the    w(u-k    of   (i.dd    erecti..n   an.' 
avoul  the  complexity  and  eonfusion  which  is  liable 
to  occur  when  a  large  nund)er  of  .lisconnected  small 
i>ars  are  used,  but  much  ,.f  the  web  niaterial   an.l 
tiic   shop   la])or   of  riveting   is   unnecessarv   for  re- 
Nistuig  stresses.  In  sonu'  of  the  designs.  Mr.  Tluu-her 
l:as  used   plain  flat   bars   adjacent   to   the   extrados 
and    intrados  placed   about    two   feet   jipart.     These 
I'ars  are  roughened  by  having  rivets  driven  at  fre- 
quent intervals,  rivet  heads  projecting  to  form  the 
luechanical  bond. 


wn 


1  20 


al:,:*ai,J":. 


COXCRETI:    BK/l>GIiS    .IXP    C[-UT'^TS. 


The  Kahn  bar  with  li«rht  comn'ctod  diagonals,  is 
v,.'ll  suited  for  ai'cli  reinforocmont,  as  the  web 
iin'inl)ers  securely  lie  the  reinfor('in<;  bar  int'  "^he 
])(»dy  of  the  areh,  but  any  sysieni  of  rough  bars  or 
rods  Avhic'h  are  completely  imbedded  in  and  sur- 
rf)unded  with  concrete  and  which  have  the  neces- 
sary cross-sectional  area,  regardless  (>f  whether  they 
have  a  web  connection  or  not,  are  suitable  for  con- 
crete arch  reinforcement. 


i     •   1     ! 


Concrete  Composition. 

It  is  customary  Avith  some  engineers  to  specify 
scNcral  degrees  of  richness  for  the  concrete  in  a 
single  ])ridge.  ^lixtures  varying  from  one  part  of 
fctuent  with  two  of  sand  and  three  of  gravel  and 
stone,  varying  through  several  different  grades  to 
corresponding  mixtures  of  1.  ~i  and  10.  are  all 
specified  in  the  same  liridge.  the  richer  concrete  for 
the  spandrel  or  arch  ring  and  the  poorer  for  the 
abutment  foundation.  The  policy  is  generally  un- 
warranted. Anyone^  who  has  observed  the  ordinary 
methods  used,  and  the  way  in  which  concrete  goes 
into  structures,  should  realize  that  exact  methods 
w'liich  can  reasomil)ly  ])e  ap[ilied  to  single  truss 
systems,  and  specifications  for  various  grades  of 
metal.  ar(>  not  ajipropriate  or  suital)le  for  use  in 
the  design  (»f  conerete  bridges,  (ienerally  it  is  ([uite 
sufficient  to  specify  oidy  one  or  two  kinds  of  con- 
ivrtv  mixtures,  the  rieher  for  the  sui)erstructure 
and  the  i)o()rer  grade,  if  another,  for  the  founda- 
tion.    Examination   of   test  records  on  the  strength 


REJXFORChD    COSCRETli    ARCH    BRIDGES.     I2l 

of  concrete  iiiixtnres,  varying  from  1,  2  anu  ;?  to 
1.  ;{  and  6,  does  not  show  enougli  variance  in 
strengtli  to  warrant  a  change  of  working  unit. 
Therefore,  instead  of  several  mixtures  witli  only 
slight  variations,  it  is  better  to  specify  a  single 
mixture.  It  is  frequently  cheaper  for  the  con- 
tractor to  put  in  all  mixtures  of  the  richer  grade, 
than  to  nmke  numerous  changes.  A  more  impor- 
tant consideration  than  the  <iuality  of  the  concrete, 
is  the  securing  <if  contact  between  the  concrete  and 
the  metal.  In  proportion  as  this  is  well  or  poorl} 
done,  the  permanency  of  the  bridge  depends. 

Loads. 

The  i)rincii)al  loads  on  masonry  arches  are  the 
dead  weight  of  the  arch  itself  and  the  sui)erimposed 
material  '>ove  it.  It  is  better  to  consider  only 
verticid  k  ,  as  acting  on  ordinary  earth  filled  Hat 
arches,  for  ihe  conjugate  horizontal  forces  are  small 
and  nuiy  be  neglected.  The  amount  of  horizontal 
thrust  from  earth  filling  is  indefinite,  for  the  earth 
will  recede  more  or  less  horizontally,  allowing  the 
arch  to  settle  at  the  crown.  Therefore,  neglecting 
liiese  horizontal  earth  pressures  is  an  assumption 
on  the  side  of  safety.  It  nuist  l)e  noted,  however, 
that  the  above  statements  api)ly  only  to  flat  arches 
when  the  proportion  of  rise  to  span  is  small.  AVhen 
the  arch  has  a  greater  rise  ecjual  to  or  approaching 
iialf  the  span,  the  conditions  are  greatly  changed, 
for  below  the  point  of  rupture  the  horizontal  thrusts 
are  so  great  that  solid  nuisonry  filling  is  required. 


UBSiL, 


m 


'  f' 
i 


12£        COSCklilli    liRllH;i-S   .1X1)    Cll.niRIS. 

The  side  rilaiiiiii<,'  walls  of  <'ar1h  filled  arches  fro- 
(luently  act  as  arch  ribs  and  earry  a  large  j)r()i>or- 
ti(»ii  oi"  the  weitiht   of  the  earth  tilling.     The  distri- 
bution  of  lo  1   earth   tilled  arehes   is  nneertaiii 
and   the    proj   ,iiion    borne   separately    by   the   arch 
ring  anti  the  side  walls  aeting  as  areh  ribs,  is  un- 
•  •ertain.     To  avoid  this  uneertainty  some  engineei's 
are    now    designing   the    side    retaining    walls    with 
one  or  more  expansion  joints  in  each  wall,  to  pre- 
vent these  side  walls  \v<,,n  having  any  areh  aetion. 
The   entire    dead    weight    and    imp(»sed    loads    must 
then   be  supported   l)y   the  ar.-h   ring.     There  is   no 
doubt   that  the   side  retaining  walls  are  capable  of 
su!)porting  large  loads  as  andi  ribs,   but   it   is  im- 
portant   to    know    definitely    which    members    of    a 
sirncture  are   in  action.     Any  type  of  construction 
in   which   Mie   action   of  stresses   is   indefinite,   is   in 
many   ways  undesirable.      The   condition    is  similar 
to  that  of  multiple  system^  for  metal  truss  bridges. 
.Multiple   systems   are    no   doubt    econoie.ical.   but    it 
is   usually   impossible   to   know   what   i)roportion   of 
the  load   is   carried   by   each  system.     This   lack   of 
definite  knowledge  is  often  the  cause  of  failure,  and 
it   is  desirable  in  the  design  of  masonry  as  well  as 
steel  structures   to   have   the   condition  of  loads  as 
nearly    fixed    as    jxKssible.      For    this    reason    many 
arches  are  designed  with  cros.s-spandrel  walls  elim- 
inating   entirely    any    possibility    of    external    hori 
zontal  pressure  on  the  arch  rinsr. 

The   weight    of  earth    filling   varies   a<-cording   to 
its  nature  from  100  to  120  pounds  per  cubic  foot, 


RELXFORCED   COXCRETE   ARCH  BRIDGES.    123 

Jind  the  weight  of  conerete  from  130  to  160  pomvls 
per  cubic  foot,  depending  upon  the  density  of  the 
stone.  Other  loads  such  as  that  of  pavement,  rail- 
ing, ^vater  pipes,  etc.,  must  be  taken  according  to 
their  actual  weights.  Approximate  general  rules 
for  moving  live  loads  are  as  follows:— 
Ci )   Light  carriage  travel  is  equivalent  to  100  pounds 

per  S(iuare  foot, 
'b)   Heavy    carriage    travel    is    equivalent    to    200 

pounds  per  square  foot. 
(c.)  Electric    railroad    travel    is    equivalent    to    500 

pounds  per  square  foot. 
'd)  Steam    railroad    travel    is    equivalent    to    1,000 
pounds  per  square  foot. 
There  is  usually  sufficient  earth  filling  above  the 
iireh  ring  to  distribute  any  concentrated  loads,  and 
particularly  for  railroad  bridges  where  the  ties  and 
rails  assist  in  spreading  the  load  out  over  a  greater 
area.     It  is  usually  safe,  therefore,  to  consider  all 
live   loads   as   uniformly   distributed.     These   rules 
apply  only  to  earth  tilled  arches,  for  the  loads  on 
arch  rings  which   have   open   cross-spandrel   cham- 
bers or  arcades  occur  beneath  the  spandrel  walls, 
and  are    plainly    concentrated    loads.     The    system 
of   loads  should    be   carefully   considered   for'  each 
ease,  and  the  designer  should  be  satisfied  in  refer- 
ence to  the  safety  of  his  assumptions,  for  local  loads 
might  easdy  occur  which  would  require  special  pro- 
vision. 

The  bending  moments  on  arch  rings  for  moving 
loads  are  a  maximum  when  the  uniform  live  load 


124        COXCRETE   BRIDGES  AXD   CULVERTS. 


I     :i 


i    >■ 


,1  -J 


covers  from  two-fifths  to  throe-fiftks  of  tlic  span, 
but  it  is  usually  eonsiderpd  as  covering  one-half  of 
tiic  span. 

The  Aveiglit  of  loaded  electric  ears  varies  from 
1,000  to  3,000  pounds  per  lineal  foot  of  track,  or"- 
half  of  this  load  being  borne  on  each  rail.  The 
weight  of  ordinary  light  electric  cars  fully  loaded 
will  not  exceed  1.000  pounds  per  lineal  foot,  but  it 
is  now  customary  to  proportion  the  better  class  of 
street  railroad  bridges  to  carry  loaded  freight  cars 
which  it  is  often  convenient  to  switch  over  electrio 
railroad  tracks.  The  additional  cost  of  proportion- 
ing bridges  for  this  extra  load  is  comparatively 
small.  The  electric  railroad  companies  themselves 
so  often  re(iuire  large  quantities  of  coal  delivered 
at  their  power  plants,  that  they  are  usually  will- 
ing to  pay  the  extra  cost  of  a  bridge  over  which 
their  tracks  run,  in  order  to  have  coal  cars  deliv- 
ered directly  to  their  plants. 

Temperature  stresses  in  masonry  arch  rings  are 
frecpiently  as  large  or  even  larger  than  the  bending 
stresses  from  partial  live  loads.  Masonry  bridges 
are  not  subject  to  so  great  a  range  of  temperature 
as  metal  bridges,  for  masonry  is  a  poorer  conductor 
of  heat  than  metal  and  the  intrados  of  an  arch  is 
not  exposed  to  the  direct  rays  of  the  sun,  neither 
is  the  extrados  or  any  part  of  the  arch  ring  ex- 
cepting the  ends  appearing  at  the  spandrel.  For 
this  reason  it  is  safe  to  assume  a  maximum  tem- 
perature range  of  from  50  to  60  degrees  between 
the    highest    and    the    lowest    temperatures    of   the 


RHixFOh'cnn  coxch'ETi-:  arc  it  bridges.  125 

ar.'h  material.  Temperature  stresses  may  be  en- 
tirely eliminated  by  the  use  of  hinges  at  the  sprinf?s 
and  erown,  but  the  praetiee  with  Ameriean  engin- 
eers is  tc  spend  more  money  in  making  the  founda- 
tions secure,  and  thereby  avoid  the  need  of  hinges. 
The  money  that  would  be  spent  on  building  liin'ges 
is  put  into  the  foundations. 

As  temperature  rises,  the  arch  expands  and  rises 
at  the  crown,  but  when  the  temperature  falls,  the 
arch  contracts  and  it  nnist  necessarily  fall  at  the 
erown.  This  rise  and  fall  of  the  arch,  due  to  at- 
mospheric conditions,  is  the  cause  of  temperature 
stresses. 

Addition  nuist  be  made  lo  the  live  loads  to  pro- 
vide for  the  effect  of  impa.-t.  The  amount  of  this 
niipact  is  determined  fn.m  the  formula 

L+D 

where  L  is  the  live  load  and  1)  the  total  dead  load 
per  horizontal  square  foot  on  the  arch. 

Units— Ultimate  and  Working. 

Permissible  Avorking  units  for  i)lain  eoncret.- 
arches  have  already  been  given  in  Part  I.  Rein- 
forc.^l  concrete  arches  nuiy  have  higher  values, 
owing  partly  to  the  fact  that  the  reinforcing  steel 
will  resist  some  compression  and  also  because  rein- 
forced masonry  is  a  more  secure  monolith.  Con- 
crete l.as  an  ultimate  compressive  stress  of  from 
2.000  to  2,800  pounds  per  sciuar.'  inch.  A  working 
unit   for  plain  concrete   in   compression   was   given 


Impact  load 


jr— ' 


U    ii 


i!   : 


\l  W  t 


,.4;; 


3  '•* 


!|^ 


120        COXCRETE   BRIDGES   .IXD   CULVERTS. 

Jit  400  pouiids  per  squai-o  inch;  for  roiiiforcod  oon- 
iTcto  it  is  s;if<'  to  J  isuiiio  r)00  poiiiicls  per  s(iiian» 
inch  for  (omijiiicd.  direct  and  live  load  bendinj; 
stresses.  For  conihined.  direct,  l)endin<>:  and  tem- 
perature stresses,  it  is  safe  to  i'ssunie  a  workiiij; 
unit  of  from  (iO/O  to  TOO  pounds  per  scpuire  inch. 

American  enjirineers  «renerally  are  accustojned  to 
nsinj?  nnich  lower  work  in-,'  units  in  concrete  than 
are  used  l)y  European  enjjineers.  There  is  probably 
suftieient  reason  for  these  lowei  units,  for  the  qual- 
ity of  work  done  in  Anu'rica  is  not  so  fine  as  is 
produced  in  France  an<l  Germany.  In  dcsi<?nin^' 
the  Grand  Avenue  bridijfe.  now  beinjr  built  in  Mil- 
waukee, the  concrete  Avorkinjr  units  used  were  r>00 
pounds  per  scjuare  inch,  and  GOO  pounds  includinir 
temperature  stresses.  IVrfeet  adhesion  of  rich 
conci-ete  to  steel  varies  from  ."iOO  to  GOO  pounds  p(>r 
square  inch.  Tt  has  already  ])een  shown  under  Hi- 
headnig-  "  A-lliesion ".  that  30  pounds  per  scpiare 
incli  of  I'xposed  surface  is  a  safe  and  usual  work- 
ing adiiesivt'  unit. 

The  ultimate  shearing  strength  of  concrete  is  400 
pounds  per  sipiare  inch  and  a  safe  working  unit  is 
50  pounds  per  squai-e  inch. 

A  safe  working  stress  for  steel  in  compression  is 
one-half  its  elastic  strength,  or  14,000  pounds  per 
square  inch  for  soft  steel  and  IG.OOO  pounds  per 
square  inch  for  medium  steel.  The  ultimate  tensile 
strength  of  good  concrete  is  200  pounds  per  square 
inch,  and  for  the  purpose  of  preventing  cracks 
forming  on  the  tension  side  of  beams  or  members 


h'fjxroh'c/.n  C(K\Ckiiii-:  akcii  bridghs.  127 


sul).i('«-f    to    heiidin?.    provision    iiuiy    be    iiiadt'    for 
tension    in    tin-   concn'tc.   tiol    cxcccdinjr  .'>()   pounds 
p<'r  scpijirc  inch.     Tli.'  oh.jccl    in  this  is   plainly   t-. 
l»n'V('nt   cracks   from   fonninj,'.   Avhich   would   admit 
water  (,r  moisture  and  expose  the  metal  to  the  daii- 
•rer  of  .'orrosion.     The   provision   is  a  safe  ojic.  but 
iis  the   modulus  of  elasticity   for  steel   is  not  more 
than    twenty   times   ^n-eater   than    for   concrete,    the 
steel    in   the   tension   side   of   the   beam   would   then 
I'e  stressed  1(.  (udy  twenty  times  the  tension  allowed 
«>n    the   concrete,    or   20    times    ,')().    which    is    l.UOO 
l»".nnds   per  s(|uare   inch,   instead  of   Ifj.OOO   pounds 
pel"  sipiare  inch. 

Some  ent,Mneers  j.ropc.s.'  a  method  of  proportion- 
iii','  c<.ncrele  sections   by   the   use  of  ultimate   units 
iipplied  to  thne  or  four  times  the  actual  loads.  This 
method  is  inconsistent.     Hrido-e  enj,'ineers  have  long 
been    accustome.I    to    usiii'?  safe    workin<r   units   for 
structures  which  are  only  a  iVaction  of  the  ultimate 
values,  using   diflPerent    working  values  where  neces- 
sary for  the  dead  and  the  live  loads.    The  same  system 
used  in  designing  steel    bridges  should  be  applied  also 
to  concrete   bridges,  and  all   sections   prop(.rtioned 
a"cording  to  .safe  working  units  after  addition  has 
been  made  to  the  live  loads  for  impaet.     It  is  evi- 
dent that  when  a  tension  unit  of  IG.OOO  pounds  pet 
square  inch   is  used   for  dead   load  stresses   and   a 
-'•'n-esponding   tension    unit    of    only   S.OOO    pounds 
'or   live   load   stresses,   that   i)rovision    is    made    by 
these  varying  units  for  impact  amounting  to  100%. 
It  is  simpler  and  more  accurate  to  follow  the  method 


3J 

A 


5;  ■ 


i  i 

li 


If 


\ 


12S 


cu.xCRLir:  uriik.i-.s  .ixn  ciwerts. 


of  tlif  iiiiii'i'  I'ccciit  sict'l  hrit'ii^c  spi'i'ificatioiis  and 
jipply  iiii|)a(  t  addition,  usiii«;  th<'  same  unit  stresses 
tor  hiitli  dead  and   live  loads. 

Theory  of  Arches. 

i'lu'  oxat'l  theory  of  arelics  is  very  complex.  Sev- 
eral coiiipi-eliciiNive  hooks  have  l)ee:i  written  on 
the  suh.ject  and  the  theory  will  be  referred  to  only 
briefly  lit  re.  For  a  frdl  discussion  and  explanation 
of  the  \aiMous  theories,  the  reailer  is  referred  lo 
any  of  the  niatheniatical  treatises  on  the  elastic 
andi.  The  sul).)cct  has  been  treated  {generally  l)y 
two  niethods.  the  analytical  and  the  graphical. 
]\I()st.  if  not  all  writers  and  designers  using  the 
analytical  nictlu><.l  follow  the  theory  as  developed 
and  explained  by  Professor  (  harles  E.  (Jreen  in  his 
l)ook  entitled  "Tj-nsses  and  Arches",  while  expo- 
nents of  the  graphical  method  use  the  one  out- 
lined by  Professor  \Yilliam  Cain  in  his  ''Theory  of 
Elastic  Arches". 

The  coniidexity  of  the  subject  is  responsible  to 
i.  great  extent  for  the  lack  of  a  more  general  in- 
troduction of  reinforced  concrete  arches.  They  {"-e 
really  a  cond>ination  of  arch  and  beam.  I'lain  con- 
•reti-  arcdies  have  already  been  discussed  in  Part  I, 
and  reinforced  conci-ctc  i)cams  are  considered  in 
Part  111.  The  reinforced  concrete  arch  is  propor- 
tioned to  act  both  in  direct  compression  and  as  a 
l)eam,  to  resist  bendinu  stresses  from  uneven  load- 
ing on  the  arch  ring. 

The  arch  is  distinguished  from  the  beam  by  hav- 
ing liorizontal  or  inclined  thrusts  at  the  springs,  in 


REISFORCi;     COXiRI.l/i    .IRCII    /iRIDGES.    129 

juMition  to  tln^  vortical   ronction  of  the  iihiitnionts. 
Arches  jirc  clnssificd  under  three  headings  accord- 
inj;  as  they  arc  fixed  or  hinj^'cd. 
(]  <  Arches  with  no  hiii<j:cs, 
(2  I   Arches  with  two  hinges  at  the  sprinj,'s. 
(3)  Arches    with    hinges    at    the    two    sjyrinjjs    and 
Jiinge  a  I  the  crown. 

They  are  chissified  also  under  two  general  heads 
into   (1     Slab  Arches  and   (2,   Ribbed  Arches. 

The  stress  conditions  in  the  arch  vary  greatly, 
depending  upon  the  presence  or  absence  of  hinges. 
The  space  allotted  to  this  book  will  not  permit  of 
more  than  a  very  brief  review  of  the  principles 
involved.  The  principal  part  of  the  computation 
for  a  reinforced  concrete  arch  consists  in  finding 

(a)  the  horizontal  thrust. 

(b)  the  end  reactions  and 

(c)  the  bending  moments  at   various  points  in  the 

span. 
After  these  have  been  found,  it  is  then  a  compara- 
tively easy  matter  to  proportion  the  metal  and  con- 
crete to  resist  the  stresses.  The  method  consists  in 
drawing  the  correct  line  of  pressure  for  th(>  given 
arch  and  loading,  and  determining  its  proper  posi- 
tion in  the  arch  ring.  AVhen  this  has  been  done,  it 
is  easy  to  find  the  bending  moment  at  any  point  of 
the  arch. 

]\rost  of  the  uneertainties  of  masonry  arches 
which  have  been  enumerated  in  Part  I  apply  equally 
to  reinforced  arches.  The  elastic  theory  applies 
not  only  to  arches  in  which  bending  moments  are 


■I  ! 


M 


iri 

u 

■i  '' 


130 


coxch'hii:  iih-iiH.iis  .1X1  >  cri.r/.h'is 


n-sist.'.l  1,\  il„.  ;,,.,. Ii  nllu^  hut  ni.iy  !».■  iiscl  iils(. 
I'nr  iin-lics  III'  si.li.l  (•.iiicirlc  with  no  fciisinn  in  any 
pnrl  of  the  ill-ell  rintr  or  when-  the  line  of  pn'ssiirc 
Ih's  in  iill  ciiM's  within  tlic  Miiddh'  tliinl  <»f  its  (lc|»lli. 
The  tiKM.iy  is  ii|)|.li.-jil)I.-  l^.tli  for  f wo-liinj;,.,!  j,n,| 
for  (ixcil  .Mid  jin-hcs. 

rcli.'s  with   fixed  cn.ls  have  live   nnknowii  .|njiii 
tilics. 

i»)   0(iui\]  hori/on1;d  thiMisIs  at   fithei-  end. 

(b)    two  v.'i'li.  al  I'nd  n-a.-tions  and 

(el   two  hcndiiiK  iiioiin-nls  at   the  sprin-js. 

Where   tlicn    aiv   no    hiiijres   in    tli-   an-h.    .!.      n-a.-- 

tioiis  are    not    tniiisl"<Tr.'d    to   tlie   ..  .ntnients   in   ae- 

eordilllce  with  the  law  of  the  h'Ver.  Sinee  there 
iire  five  nnknown  (|nii(itities.  th.-n-  must  in  additi.>n 
to  the  two  ('(luatioiiHof  e(|iiilil)riiiin.  :ia-=^0an(12i>  0 
l)e    llu-ee    nion"    e.|niiti..ns    round.      These    are    d.-ter- 

iiuiied   from   the  iditions  (.f  e(|Milil)riniii   for  Hxod 

end  iirehes.  wliieh  ;ire  as   follows:- 

(1,1   The  jinjrle  of  inelination  thai   the  spriiijrs  make 

with  eji'-h  other  must  not   ehan^'e. 
(2)    The    relative    elevation    of    the    two    end    ahut- 

moiits  must  not   eh;in<jre.  and 
(;^^   The  let^th  of  s|)an  iiuist   not  .•Imiiire. 
These  are   mathenuitiejdiy  expressed    by  the   f(.rmn 
lae : — 

:i^iM     0,  :i7,«Mx     0,2:f,nMy    n. 
In  the  above  foruudae.  .M   is  the  jjeueral  value  of 
the  bendin<i  niomenls.  u   flie  ien^'th  of  a  short  por- 
tion (.f  the  areh  rinj,r  an<l    x  find  y.  the  horizontal 
and  vertical  coordinates  to  iJie  center  of  n,  nieas- 


R/:i.\rORCEP    COXCRETIi    ARCH    BRIDGES     131 


tin'd  from  the  (>ri<riii  jit  the  s|>riti),'H  A  or  H.  Kixi'il 
end  arches  have  hi^h  l('iu|)eraliire  stresses,  tw..  to 
four  times  greater  tliaii  for  t\vo-hinjri'<l  arches. 

The  abutment  reactions  for  ardies  with  either 
two  or  three  hin<,'es.  i'oUow  the  law  of  the  lever, 
vvhi.'h  greatly  simi)lilies  the  mathemntieal  ealeula- 
tiotis. 

Two-hinged  arches  have  only  three  sets  of  un- 
iviiown  forces. 

(]}   The  horizontal  reaction  and 
(2     The  two  vertical  end  i-(\ic'tions. 
'is  there  are  hinges  at   the  end  and  a  condition  of 
continuity   cannot    exist    there,    the    two    additional 
unknown  quantities,  the  two  unknown  beiuling  mo- 
uicnts  at  the  springs  do  not  now  exist.     This  is  the 
theoretical  a.ssuinption,  but  it  is  not  exact,  for  even 
with     pin     bearings   at    the   end.   there    is   a   large 
amount  of  friction  on  the  nins  and  the  bending  mo- 
ments will  not  entirely  disappear.     The  assumption, 
hoAvevcr.   for   two-hinged    arches    is    that    there   are 
tinly   three  sets  of  unknown   forces.     Therefore,    in 
addition  to  the  two  usual  eciuations  of  e(iuilil)rium 
^>      0  and  ^y  =  0,    there  is  only  one  other  eipia- 
tion  required,  and  this  can  be  found  from  the  cun- 
dition  that  the  length  of  span  must  not  change.  The 
span   length   should    not    change   or   no   sliding  of 
either  abutment  should  occur  in  order  that  the  arc'i 
ring  between  the  springs  shall  remain  intact. 
The  third  e(iuatiou  reiiuired  for  the  solution  of 


1 


iiii 


1^ 


f : 


1 


5.3 


•,  ;  I 


132        COXCRETE   BRIDGES   AXD   CrL]-ERTS. 

the  two-hinged  arch  is.  therefore,  expressed  as  fol- 
lows : — 

2UM^    0 

Hinged  arches  are  not  fre(iuently  built  in  America, 
hut  some  designers  for  the  purpose  of  simplifying 
ejilculations,  consider  the  arch  ring  as  hinged  at 
the  springs. 

The  condition  of  stress  in  three-hinged  arches  is 
definite,  for  the  moments  both  at  the  springs  and 
crown  are  zero,  and  the  position  of  the  line  of  pres- 
sure is,  therefore,  fixed  at  these  three  points.  Tlic 
equations  of  equilibrium  for  three-liinged  arches 
are,  therefore : — 

2fx  =  0,   vj/  =^  0,  :^M  =  0, 

The  thrusts,  bending  moments  and  shears  may  be 
found  most  easily  by  Professor  Cain's  graphical 
method,  after  which  the  section  may  be  most  easily 
proportioned  analytically.  It  has  already  been 
stated  that  the  graphical  method  consists  in  draw- 
ing the  correct  line  of  pressure  for  the  given  arch 
and  loading  and  determining  its  proper  position  in 
the  arch  ring. 

The  following  method  is  used  for  determining 
the  form  of  arch  and  the  thickness  of  the  arch  ring 
for  uniform  loading.  It  avoids  the  usual  trial 
method  given  in  Part  I  for  solid  concrete  arches. 
The  position  of  the  springs  must  first  be  as.-:nmed 
as  well  as  an  approximate  crown  thickness  and  the 
depth  of  earlh  filling  above  it.  The  remaining 
height   from   spring  t(»  crown   intrados  will  be  the 


'  .j^^i^i^^&ii^^imrftiiSL^     ^i™ki .. 


-•.■v>...*A. 


REIXrORCED   COXCRRTE   ARCH   BRIDGES.    133 

rise   of   tho    ;irch.      The    method    (Icp.Mids   upon    tlio 

equation,  M     HT,  wlunv 

M  is  the  bcndiiifr  nioment, 

H  the   erowii    thrust   or   poh'   «list;in<-<'   of  the   foree 

polygon,  and 
T  tlie  verticjd  ordinate  to  the  pressure  curve  at  the 

point  where  the  moment  is  taken. 
The  hending  moment  at  the  center  is  tlie  same  as 
for  a  simph>  ])eai;i  and  dividing  this  moment  by  the 
areh  rise  gives  the  crown  thrust  or  pole  distance 
II.  The  bending  moment  at  any  other  point  of  the 
•irch  is  e(|ual  t(^  the  imle  distance  II  multiplied  by 
the  vertical  intercept  at  that  point  in  the  funieular 
I-olygon.  The  moments  are.  therefore,  computed 
for  as  many  points  as  desired  and  dividing  these 
moments  l)y  the  pole  distance  II.  which  has  already 
been  found,  gives  the  recpiired  ordinates  T  to  the 
funicular  polygon,  which  is  tlu«  line  of  pressure  for 
the  full  assumed  loading.  The  pressure  curve  is 
then  plotted  from  the  ordinates  found  and  this  will 
give  a  curve  for  uniform  loads. 

The  height  T  referred  to  above  is  the  distance 
to  the  line  of  pressure  measured  from  a  horizontal 
line  through  tlie  point  of  rupture,  wiiich  is  not  nec- 
essarily at  till'  abutment  face.  The  correct  crown 
thrust  cannot  be  obtained  l)y  using  a  distance  T  to 
any  point  below  the  point  of  rupture.  When  the 
point  of  rupture  falls  within  the  abutment  face, 
the  span  lenglh  must  Ije  taken  as  the  distance  be- 
tween the  points  of  rupture,  and  not  the  clear  dis- 
tance between  abutments. 


f' 


hi 


>i 


•  I 


\ 


I  i  t 


(3 


II: 

III 


3; 

5: 


14- 


l.*?4        COS'CRETE   BRIDGES  AXD   ClIJ-ERTS. 

For  full  (.lead  and  live  loads,  the  line  of  pressure 
should  wherever  possible,  lie  within  the  middle 
third  of  the  arch  rinj?,  and  reinforcement  used  oidy 
for  resisting  bending  stresses  due  to  partial  live 
loads.  In  Figure  20,  the  weight  of  the  arch  ring 
may  be  assumed  at  its  mean  thickness  at  the  quar- 
ter point,  and  the  arch  ring  weight  assumed  ap- 
proximately as  a  uniform  load.  The  weight  of  earth 
filling,  pavement   and   other   material   between    th" 


extrados  and  roadway  levci.  as  well  as  the  uniform 
live  load,  is  also  uniform,  and  the  center  bending 
moment  for  these  uniform  loads  is  expressed  by  the 
equation: 

W  S' 


M. 


8 


For  a   parabolic    arch,   the    spandrel    area    shown 


l! 


«iiJ!'?fc^?S^ 


REI\ FORCED   COXCRETE   ARCH   BRIDGES.    135 


hatched  in  Figure  2G  is  equal  to  ^^.  The  center  of 

6 

gravity  of  this  area   is  e(|nal  to  one-eighth  of  the 

span   length   from   the   al)utnient    face.      Therefore, 

the   l)encling   moment   at   the  center  from  spandrel 

25  R  S" 
filling  is  equal   to   — The  total  moment  is, 

therefore,  equal  to  the  sum  of  moments  from  uni- 
form loads  and  from  the  spandrel  filling.  Dividing 
the  center  moment  by  the  rise  gives  the  crown 
thrust  or  pole  distance  K  for  the  force  polygon. 
Thi'^  is  a  very  convenient  analytical  method  for 
determining  the  correct  arch  form  for  any  system 
or  arrangement  of  loads.  A  combination  of  the  an- 
alytical with  the  graphical  method  will  simplify 
computation,  as  some  results,  like  finding  the  crown 
thrust,  may  be  determined  most  easily  by  the  an- 
alytical process. 

In  practice,  it  is  usually  sufficient  to  find  the 
sum  of  all  moments  and  thrusts  at  three  different 
points— the  center,  the  quarter  points  and  springs. 

The  thickness  of  arch  ring  at  other  points  below 
the  crown  must  be  such  that  the  vertical  heights  D, 
shall  not  be  less  than  at  the  crown. 

The  bending  moment  at  any  point  of  the  arch 
ring  from  partial  loading  is  equal  to  the  pole  dis- 
tance or  horizontal  thrust  at  the  center,  multiplied 
by  the  vertical  intercept  between  the  neutral  plane 
and  the  line  of  pressure  at  the  point  considered. 
Tiic  correct  position  of  the  line  of  pressure  for 
partial  loading  will  already  have  been  drawn  upon 


I:  ^i  I 


\  \ 


HI 


■I 


:i" 


! 
i  I 


*4* 


13G        COXCRETE   BRIDGES   AXD   CULVERTS. 

the  arch  ring,  and  the  vertical  intercept  may  bo 
scaled  and  will  be  positive  or  negative  according 
as  the  pressure  curve  lies  above  or  below  the  neu- 
tral axis  of  the  arch. 

The  determination  of  the  thrusts  and  moments 
may  be  simplified  l)y  considering  the  arch  as  a  par- 
abola. This  is  approximately  true  when  the  rise 
is  small  in  comparison  to  the  span. 

The  stability  of  an  arch  is  secured  when  it  will 
resist  the  stresses  resulting  from  thrust  and  bend- 
ing from  any  system  of  loads,  x^hen  the  line  of 
pressure  is  drawn  in  such  a  iiosition  as  to  produce 
the  least  possible  bending  moment,  or  when  the 
line  of  pressure  is  drawn  the  nearest  possible  to  the 
eenter  line  of  the  arch. 

General  Design, 

The  introduction  of  bridges  of  combined  metal 
and  concrete  has  thrown  open  a  wide  field  for  im- 
provement in  design.  So  long  as  it  was  necessary 
to  build  bridges  of  stone,  the  art  showed  no  great 
i'uprovement  over  the  Avork  of  the  ancients."  In 
recent  year^.  however,  the  increa.sed  i)roduction  of 
cement  Avill,  its  decreased  cost,  as  well  as  the  in- 
vention of  improved  stone-crushing  machinery  and 
appliances  for  mixing  concrete,  have  tended  to 
)nake  larger  structures  possible,  even  in  solid  ma- 
sonry. The  greatest  j;rogress  in  the  art  has  been 
made  since  the  completion  of  the  Austrian  experi- 
ments in  18!).").  Ki'inforced  concrete  has  made  it 
possible  to  discard  old,  conventional  forms  and  to 
introduce   new   and   lighter   types   of   bridges   sup- 


■^SF^N^E^ 


REINFORCED    COXCRETE   ARCH   BRIDGES.    137 

ported  by  arch  ribs,  carrying  open  spandrel  framing 
to  support  the  roadway.     The  enormous  reduction 
in  the  dead  weight  of  the  superstructure  has  caused 
a  i.roi,ort,onateIy  large  saving  in  the  foundations. 
A   large  nund)er    of    improved    methods  of  design 
have   already  been   tried  successfully  and   there   is 
prospect  of  additional  progress  in  the  future    With 
the  new  material  designers  are  following  to  some 
extent  the  outlines  used  for  metal  bridges,  so  there 
me  now  inimerous  examples  of  bridges  built  in  con- 
••rete-steel,    not    only   in   the   form   of  light   ribbed 
arehes,    but    also   as   solid    and   ribbed    cantilevers, 
girders,  trusses,  etc.     The  new  material  is,  in  fact 
being  used  according  as  its  own  properties  will  per- 
mit. ^ 

The    general    subject    of    arch    bridge    design    is 
divided  nito  four  parts, 

(1)  The  parapet  or  deck, 

(2)  The  spandrels, 

(3)  The  arch  ring  and 

(4j   Temporary  arch  centers. 

In  beginning  the  general  design,  the  final  object 
•should  at  all  times  be  kept  in  view.  The  first  and 
•■Hi''t  object  in  building  all  bridges  is  to  construct 
^>id  support  a  platform  at  the  proper  elevation,  of 
suihcient  capacity  to  safely  and  securely  conduct 
travel  over  certain  openings.  A  second  object 
which  is  too  often  neglected,  is  the  desirability  of 
making  the  bridge  pleasing  in  appearance,  in  har- 
mony with  Its  surroundings  and  a  credit  to  its 
builders. 


Ikxl^; 


11  ;i 


r- 


I  A  ri  li 


1>   COSCKETE   BRIDGES   A\D   CCLrERTS. 

AVhe.i   ',;;•!•  started,  the  tlt'sigii  should  he  eontiu- 
iied  in  logical  sefjucnee.     The  width  of  hridge  and 
the  kind  of  pavement  reiiuired,  should  be  selected 
with  tJie  necessary  filling  beneath  the  pavement  to 
support   the   roadway   or  the   railroad   ties.     After 
deciding  upon  the  kind  of  deck  required,  the  most 
economical   method   of  sui)porting   this   deck   must 
be  determined.     It  may  be  carried  on  solid  earth 
filling  or  on  a  series  of  walls  or  columns,  and  these 
may  be   continued  to   the   ground  in   the   form  of 
a  trestle,  provided  the  height  from  deck  to  ground 
is   small.     If  the   height   be   great,   these   walls   or 
columns  may  then  be  supported   on  other  ribs  or 
frames,   such   as   arches   or   trusses,   and   the   loads 
from   these   may   in    turn    be    transmitted   to   the 
ground  through  Malls  or  piers  of  the  most  econom- 
ical form.    There  is  no  good  reason  why  the  span- 
drel columns  of  a  concrete  bridge  cannot  be  sup- 
ported in  other  ways,  excepting  on  slab  or  ribbed 
arches,      "^'russed    frames    or   girders    are    possible 
forms,   though   they   would   not   be  as   pleasing   in 
appearance   as   a    continuous   arch.     It    is   possible 
that   arches  with  double   ribs   or   drums  separated 
by  systems  of  framing  may  be  used,  following  the 
outline  of  a  double-braced  metal  arch.     If  the  de- 
sign  is   developed   in     successive    steps,    beginning 
with  the   roadway  platform,  and  transmitting  the 
loads   continuously   in    the    most   economical    man- 
ner through    various    kinds    of    framing   into   the 
foundations,  the  result  will  be  both  scientific  in  con- 
struction and  satisfying  to  the  engineer.     It  is  a 


Mi7^' 


.•.A-     ■i.-^fst' 


REINFORCED   COX  CRETE   .IRC  1 1   BRIDGES.    139 


drplorablo  fact  that  tlio  design  of  many  bridges 
is  begun  by  first  b.eating  the  foundations  and  de- 
veK)ping  the  design  upward  froni  the  ground,  in- 
stead of  from  the  deek  downward.  This  one  error 
aeeounts  for  the  absence  of  economy  in  many  struc- 
tures. 

The  old  empirical  rule.s  for  masonry  arches, 
which  required  more  masonry  in  the  abutments 
than  in  the  arch,  are  unscientific  and  useless  for 
reinforced  concrete.  All  through  bridges  are  ob- 
jectionable. They  are  a  menace  and  an  obstruction 
to  travel,  are  lacking  in  lateral  stiffness,  and  the 
trusses  or  framing  interfere  with  the  river  view, 
which  is  generally  and  should  always  be  an  inter- 
esting feature  of  a  river  bridge. 

If  a  bridge  has  several  spans  and  one  span  has 
movable  bascule  leaves  or  other  kind  of  draw,  the 
»)utline  of  the  draw  span  should  conform  and  har- 
monize with  the  rest  of  the  bridge  and  its  pres- 
ence should  be  indicated  by  piers  or  towers  at 
cither  side  of  the  opening.  The  underneath  out- 
line for  double  bascule  leaves  in  a  single  span  may 
easily  be  made  in  the  form  of  a  continuous  arch, 
corres|)onding  to  the  intrados  curves  of  other  spans 
in  the  bridge. 

rnsymmetrical  arch  spans  may  be  used  at  the 
ends  of  viaducts  cro.ssing  deep  ravines.  They  cause 
a  large  .saving  in  the  abutments  by  permitting 
higher  springs  at  the  abutments  than  at  the  piers" 
The  half  shore  span  adjoining  the  pier  may  be  made 
with   intrados   curve   to   correspond   with  the   next 


if' 


i-»(» 


(■(>\CR/.i I-:  nkinci-.s  .ixn  cr/.i  /  rts. 


ailjomiMK  spmi.  flm,  pn„l„M„jr  syunnctrv  ;,l,nuf  the 
!"<•'•  "■"I<"r.  As  tl...  ,.,hI  n,v|,  spai.  Ii,.-ks  svinim-trv 
111  th."  ;in-h.  it  is  M.M-.ssary  f(.i- apiM'arancc.  that  tli".- 
(l''sij,'ii  sliail  he  syiiiUM'trical  about  the  pi.-r. 

Til..  Kissi.ijrn-  ilri.I^'...  twelve  ,„iles  soi'Mieast 
»i*"iii  Wal)asli.  IiMliaiia.  is  ,.f  mmsiial  <lesij,Mi.  It 
liiis  a  l(;-r.,..t  eunerete  n.a.lwav  slab  halaiieed  ...i 
a  sin-le  ernter  eonerele  wel,  12  inehes  in  Ihiek.iess. 
supported  on  a  sej^iiiental  eonei-ete  areli,  S  feet  in 
\VKltli.  It  is  a  sin<rle  span  liijrhway  hridj^e.  with 
'•O-loot  openin-r  ami  was  built  in  1!)()7. 

All  town  or  eity  bn,ljr,,s  should  have  open  ehani- 
bers  beneath  the  Hoor  for  pip,,s  and  wires.  They 
may  either  have  removable  iron  eovers,  or  })e  pa  veil 
over,  with  maiili..].-s  or  entranees  provided  at  either 
ond. 


Hinged  Arches. 


Then 


!•<'  IS  a  din'erenee  of  opinion  with  regard  to 
;i";  use  of  hinjred  or  fixed  arehes  for  ii.asonrv 
l>n«!^^.'s.  llu.^vs.  by  whieh  is  meant  the  insertion 
<'l  iH;.ivy  ston.  or  in.  tal  bh,eks  at  ..r  near  the  een- 
trr  line  ot  the  aivh.  remove  one  of  the  priueipal 
uneertamtles  of  arch  eouslrueti..n.  bv  tixin-  the 
posit  Km  ',!•  th..  lin..  of  pressure  at  the  springs"  The 
"'ivsenee  of  a  Iiin-,'  at  the  erow.i  tends  to^.-onsid- 
'■ni  il.v   reduce   the   n-idity  and   inen-as-  derieetion 

••nid  IS  m)t  ahxays  to  !,e .mimen.led.     U\u<n^s  may 

hv  introduced  at  th.'  s,,rin-s  in  sm-h  a  manner  an 
to  lusnre  absolutely  v.  it  bin  small  limits  the  posi- 
tion ot  the  line  of  pressure  there.  Fixed  ends  tend 
to   greatly    nu-rease    the     amount     of    temperature 


RHINFOKCr.D    COXCRin/i    .IRCIl    HRinCES.    141 

stivss.N  and  llu-y  hav,.  „„  advai.ta-.'s  ..vcr  |,i„jr,.,l 
•'IkIs.  Alt.T  f|„.  .-..nhTs  an-  n-iiiuv..,!  an.l  the  arcli 
r-nifT  has  ,.(„„.■  t(.  ,.,•  nraH.v  to  its  final  pcsition  the 
-P'-n  .loints  at  the  hin-.-s  should  th.-n  he  tiUfd  s„li,l 
with  ...MHcnt.  so  tl...  .Mitiiv  ,.ross-s,.,.tion  at  thr 
liin-."s  wdl  h.-  availahl,.  f„r  f„ll  h.adin-.  The  pros- 
">i(M'  or  hinjres  or  th.'  assumption  nf  th.-ir  pivsouce 
Id   111.'  spring's,  siniplifit's  the  (•on.pntati<.ns  and  re- 

'"••'■''•^   ""<"   "»■  tl l'i''f"    uncertainties   of   eonerete 

"'■'•'.'   •'''•^'^'"-     '''"'   AoH'i-iean    praetiee    has    been   to 
av(Md  any  .>xtra  expenditure  on   hin-es.  hut  to  jmt 
It     into    the    foundations,   insuriufr    their   stability 
ajrainst    niovenuMit.      Then-   are   nunu'rous   unfortu- 
>'Jde    (.as.'s    Mhere    the    foun.h.tions    hav    been    in- 
suttieienl.     Several  spans  of  a   bridge  over  the  Illi- 
nois Kiver  at  I'eoria  were  nvenlly  destroyed,  owinj; 
to  the  undermining  of  foundations.    Hinges  are  de- 
sirable  ehieriy   where   it    is   k„(.wn   that  "the   soil   is 
yielding  and  the  abutnuMits  ar.'  liable  to  recede  lat- 
''i-ally.  allowing  the  arch  to  fall  at  the  crown    and 
cause  inisightly  and  possibly  dangerous  cracks      A 
method   employed    by   certain   (i.'rmau   engineers  is 
to  place  hinges  at  the  point  of  rui)ture.     This  was 
•1"""   "1  a  bridge   built  at  Kempten.  Bavaria,  over 
"'•'    lller   River,   and   described   in   the   Engineerinjr 
News.  .May  2,  1907. 

Ribbed  Arches. 

The    principal    economy    in     reinforced     conorete 
bridges  comes  fro?n  the  use  of  ribbed  arches.    Most 
of  the  surplus  material,  both  in  the  structure  itself 
and  in  the  spandrel  filling,  may  then  be  eliminated,' 


*  ! 


m 


"2     coxCKiiir.  iiKin<;i:s  .ixd  cn.niKTS. 


I   I' 


i!    ,- 


if' 


and  as  wcijjlit  ol'  siiiMTstnirturc  dec  rouses,  Ihc  cost 
of  foundations  dtcrcahes  in  proporti(»n.     The  use  of 
ribs   instead  of  slabs,   is  a   more  scientific   type  of 
construction    and    allows   the   strongest    supporting 
nieiuhers    to     he     placed     exactly    where    re(|uirod. 
Kihbed  concrete  arches  are  purely  a  product  of  this 
new  material  and  are  possible  in  concrete  only  when 
properly   reinforced    with    metal.     Concrete   ribbed 
bridges   are    built    mostly    in    the    form    of   arches, 
though  other  forms,  as  cantilevers,  have  also  been 
used  with  varying  degrees  of  success.  :Many  bridges 
designed  as  arches  have  cantilever  action  also,   or 
when  the  rise  is  small  in  proportion  to  the  span, 
the  stresses  are  chieHy  the  result  of  bending,  and 
regardless  of  theory  the  span  acts  then  more  as  a 
beam  than  as  an   arch.     The  uncertainty  in  refer- 
ence to  cantilever  or  !)eam  action  of  arches  can  be 
removed  by  building  an  open  vertical  joint  between 
the   arches  over  the   piers,   the   presence  of   which 
will  positively  prevent  any  cantilever  action.  "While 
such   a  joint    removes  a  seriiuis   uncertainty  of  de- 
sign, it  is  very  doulitful  whether  or  not  this  expedi- 
ent is  desirable,  for  the  cantilever  action  frequently 
adds   as  much   strength   to   the   bridge   as  does   the 
.irch  and  when  properly  designed  and  built  to  re- 
sist both  sets  of  stresses,  the  i>resence  of  canti         r 
action  adds  greatly  to  its  strength  and  permanence. 
The    Walnut    Lane    bridge    at    I'hiladelphia.   and 
the  Rocky  River  and  Piney  (reek  bridges  now  un- 
der construction,  illustrate  to  some  extent  the  sa\- 
ing  which  may  be  accomplished  by  the  use  of  ribbed 


i; 


Ijl 

•  {  ;; 

"  i' 

1  c 

'1? 


144 


(  '  >.\  (  A7;  / /;    liUll<u!-s    .1     It    ,  I  lAI  ■•TS. 


iM  pl.-icc  of  sK.I)  ar.lirs,  ,in.l  yd    A\  ..f  tins.,  tliivo 
»»ri(!f;..s  nrv  only   M.-.rtiiilly   til>l..'.'      Tl..  y   .  ,rh   .■..!i- 

Slst     (.r    Jl     |,;,;i-    nf     luii,     jipch     ri|._'S     S.-Jlil!, ;'     ,1     !    ^-      i 

•''^^"" »■    '■'■'■"!     10    tu    L'O    IVrl.     whi.i      .;.„.         ]..- 

tu.'.Mi    the    1    r.sfs    is    spiinncd     l.y    siniplr      i,.,,,-    ,     ,,- 
stru.'ficr        Tlh    wavitiK'  in  tli.-  a.vli   riny  i.,-  i],;^  .  ^. 

("•(li.Mii  ,.  fn.ni  2:.  :  to  :{(k;  ,..  ,i,,.  ,.,,st  of   * ,.  .-ii  - 
whi.-h   sji   iiijr  would    i...  <till     nrllH      m,-        ,.,1   iT 
using  ...    in-  ril,l„  ,1  ,|,.si-n-      Tlh    I.,,  .,  ,„l„.r-  .ton 
arch    bn.lp.    i-i   (icrniany       itii   a   M.a:     of  27:    fc. 
and  (onipl.-tcl    n    h.-  y.-ar  I'm:{,  j.  ,',f  ,     ,  x.,„„,    ,., 
An    unusual    .'xaniplc    ,,f    rii,!M.,j    ,.,,vi,    .i,.s,^,„    .„,, 
pared   l.y   Mr.   Turner  of  Mi,,    ,.;,., oii-         sh.  Wi 

Figure  27.      Ft   is  one  <.f  sev.      1  ',1,..;^.,      ^ub.  ,1 

i-i    the  I'rand  Avnue  \  i,,du,       n  y     ...     ,1,  .  he 

Tuain   eonipressi-n   nie-ibc!  ■<   ai-    .x-ta-ou  ,1 
hoojH'd. 

Tfn-  use  of  ribs  instead  of'  slah^  makes  it       ,ssihle 
to  phu-e   niend)ers  ol'  the  piui,.  r         -nL'tl  ■,.  p,.- 

•  luired,  as  for  exanipir  uiui   v     nes  uf  .  \y    y 

trark.  M-h.T,    heavier  ribs  are  ii<ually  i  .,i  tl      i 

under  other  parts  „  ih.-  r,  mUv-.^v  'si.i.--  .i^.  ,„.  ,. 
be  braekete.i         u,  ti.  .    Hb.  „n.I   ^n    .erlv  tied 

into  or  across      le  ('<>        .    ,,   the         ole       si-n  exe- 

'■"l!;^'  '"  ;'  ""     '  ^"'  •  ^"      oniical  manner. 

Uw  pnncit>a,  obje.  •  n  to  m-  u^e  of  ri'.s  is  the 
extra  cost  ui  ii,  required  ooden  f  as.  vhich  of 
<.nu-sc,snu..b  greater  i.,  for  pj.dn  .v  d  slabs. 
Notwithstandn:  -  this  obi.    tion.   impo,  eonerete 

ar.-h.s  ol  the  ,ure  will  possibly  b^.  ,  uilt  with 
nbs.  partieidarl:  ^vhen  le  proportion  of  the  rise 
^o  span  IS  larg-e. 


tre 


klilXlUh    ,:!J    COXCRI.TE    .11  CH    PRUXil-S      H^ 

Intrados  Form. 

A  low  lliit  ..pcniiiK  is  the  best  form  f'.r  Wv  p.is- 
^'''-"  'I'  «  f.  A  roctjingiilar  opfiiirifr  >r  eii! verts 
with  tlu-  hciijlit  i,'n'atcr  tluin  the  widt!  wiH  cost 
1<-  than  when  the  width  is  the  groat. t  of  th»-  two 
(111,  I'll  lis.  This  is  <'h'arly  show  by  the  <  ulvert 
<lcsi}.'n  t-iv.',,  in  Tiihlcs  VH,  VIII,  IX  and  X  (.f 
Pat'  I\',  I  lit  tiw  (hcn-asod  cost  is  secured  a.  the 
expense  (        (Ificiciicy. 

Iiitradii  Ills  should  be  as  nearly  as  possible  ex- 

;i<  t  math.  ,,iical  curves,  but  if  shcse  cannot  l)e 
MM-ured,  tiny  should  I  lien  approad  so  nearly  to  the 
•  xact  curves  that  tin  lack  of  re<rnlarity  may  not  be 
detected  hv  the  ey-.  Three  an<l  five  centered  Hat 
arches  as  pproximation  to  the  ellipse,  are  usually 
unsalisfa'-  \-\  because  the  breaks  in  the  curve  can 
''^'  tlp^  if  a  Hat  ellipse  is  desired,  the  curve 

exact  ellipse  and   not  an  approxima- 
which  are  too   flat  are  not  artisHc. 
nil. -fourth  t..  one-sixth  of  the  span 
•r  appearanc(>.     Natural  conditions 
or    grade    lines    will    frcpiently   prevent    even    this 
amount  of  rise,  ami  it  must  then  be  determined  by 
stability    rc.piiremeiits.    which    should     not    be    less 
than  fi'.)!)!  oiie-ei,<,'hth  to  one-tenth  of  the  span.    The 
st(>el    arch.s    of   the    bridge    across    the    Mississippi 
Kiver  at    St.   Louis  have  a   rise  of  one-eleventh  of 
the  span  and  then;  is  at  Stcyr,  Austria,  a  reinf 
e..n.-rete   bn.lge  of  ]:J!)-foot  span,  the  rise  of 
is  only  one-sixteenth  of  tlie  opening. 
Earth  filling  in  the  haunches  tends  to  m. 


sliouh 
tioti.      K. 
A   ris.'  ol 
will  give 


*  I  * 


miMH 


li  »! 


1    |l 


■    ^ 


■  m 


146        COXCKIiTE    BRlDCIiS  .1X1)   CVLVEKTS. 

lino  oF  pi-i'ssurc  jipproacli  the  form  of  an  cUipst", 
while  the  nnifonn  loads  including  the  weight  of 
arch  ring,  filling  above  the  extrados,  pavement  and 
full  live  load  lends  to  depress  the  line  of  pressure 
fo  the  approximate  form  of  a  parahola.  The  eom- 
I)in('d  etf'eet  of  these  two  tendencies  is  to  produce 
H  curve  ai>i)roxiinating  a  circular  segment.  The 
resulting  curve  will  lie  nearer  to  the  ellipse  or  to 
the  parabola,  according  as  the  effect  of  haunch  fill- 
ing or  uniform  load  predominates. 

The  trial  method  of  determining  the  intrados 
curve  is  no  longer  necessary,  for  a  direct  method 
has  been  given.  Under  the  head  of  "Theory  of 
Arches'',  a  method  has  been  explained  for  deter- 
mining the  amount  of  crown  thrust  by  dividing  the 
center  bending  nion)ent  by  the  rise.  The  simple 
beam  moment  at  any  other  point  is  ecpial  to  the 
crown  thrust  or  pole  distance  II  multiplied  by  the 
vertical  ordinate  in  the  funicular  polygon,  which  is 
the  intercei)!  b<twecn  the  closing  line  and  the  pres- 
sure curve.  Therefore,  dividing  this  bending  mo- 
ment i)y  the  crown  thrust  or  pole  distance,  gives 
the  prop"r  ordinate  or  rise  for  the  center  line  of  the 
arch  at  the  point  considered.  This  method  makes 
it  iiossible,  after  having  first  assumed  the  approx- 
imate form,  to  di'termine  directly  without  trial,  the 
exact  intrados  curve  for  uniform  loading.  AVhen 
the  exact  linear  arch  has  been  found,  the  bridge  will 
present  a  bett"r  appearance  if  a  regular  curve  be 
tlrawn,  such  as  a  segment  or  ellipse,  even  though 
the  use  of  a   regular  curve  makes  the  arch  some- 


ia 


RE/XI'Oh'CJ:.') 

lOXCRliTIi    .IRC  1 1 

BRIDGES. 

147 

wilt 

t    thicker 

ill 

certain 

parts 

tha 

1    is 

requi 

red. 

Aft 

•r   haviiij? 

drawn    the 

correct 

linear 

arch, 

the 

tiiicUtiess  of  tlie  ring  for  uniform  loads  should  l)e 
proportioned  directly  to  the  thrusts. 

The  computations  are  much  simplified  if  the 
curve  be  considered  a  parabola,  aiul  this  assumption 
is  api)roximately  true  when  the  rise  is  small  in 
comparison  with  the  span.  Parabolic  and  seg- 
mental arches  require  little  metal  reinforcing,  while 
elliptical  and  other  fiat  arches  may  require  a 
greater  anu)unt. 

Some  designers  prefer  to  use  an  intrados  curve, 
lying  half  way  between  a  segment  and  an  ellipse 
and  found  by  bisecting  the  vertical  intercepts  be- 
tween these  two  latter  curves.  'Sir.  Burr's  Potomac 
Memorial  Design  No.  3  has  an  elliptical  intrados, 
with  a  rise  of  one-fourth  the  span,  and  a  segmental 
extrados. 

Spandrels. 

The  principles  already  given  for  the  spandrel  de- 
sign of  solid  concrete  arches,  apply  also  to  arches 
of  reinforced  concrete.  If  side  spandrel  walls  are 
used,  provision  should  be  made  for  expansion  or 
these  side  walls  will  crack.  A  dovetailed  expan- 
sion joint  is  the  most  satisfactory  one,  for  sufficient 
space  can  be  allowed  in  it  for  expansion,  while  the 
two  wall  sections  are  held  securely  together.  If 
an  expansion  joint  is  not  provided,  an  open  crack 
is  liable  to  develop  between  the  spandrel  wall  and 
the  arch,  and  if  an  effort  be  made  to  prevent  such 
an  opening  by  clamping  the  spandrel   with  metal 


T^?  1('rj«P^HPr,««ra«i 


■Hi 


148 


t 

Ml 

; 

fi 
li 


I 


[' 


1' 

1! 


!  , 


•I 


COXCRP.ri-.    BRIDciis    .IX D    Cl'IJ-ERTS. 


^^^'^  lo  11...  iMvli  rin^r.  ,i„.  ,,,,.,,  i„  ^,„.  .,^.^.,^  j,^^.^^ 
''<■';;•>"<•..  iml.h.nMiM.l...  .s  ;.  portion  „t'  t!,,.  W.u\ 
•»v.      I,r  .-Mrri.Mi   by  ll.r  mv),  ;,<.ii,>„  „r  ,,,,  s,,;,n,l,vl 

Willi. 

-'••inls  in  .MMitimions  wmIIs  should  on-ur  sit  in- 
te-rviils  nol  (■x.M-,.(|i„j:  20  f,,  25  feet.  Jt  has  bccM, 
;onn.i  l,y  rxponc.,,.,.  llmt  t.M.UHT.tnre  cracks  occur 
m  solul  Malls  at  al.ont  these  int.-rvals  and  if  artifi- 

•■"    •."•'"^•^  •'*'   '■'"•""•<'•  <l'<'  ^l.'vcloping  ,>f  unsi^M.tlv 
{"ii.l  inv-nlar  .-racks  will  he  avoided. 

All  expos..d  flat  c..n<-r..te  s-.nfa.H's  slioidd  he  pan- 
H(''l  lo  av..id  nion..t..ny.  If  is  ditTi.-nlt  to  build 
plain  surfaces  perf.vtiy  straight  or  pl.nnb,  and  tho 
use  of  panels  with  pilasters  and  b.dt  courses  assists 
to  c.n.eeal  irregularities  an.l  in.perfe,.ti,.ns  in  Hat 
■surfncos,  that  otherwis,-  might  be  .p,ite  apparent. 

Open  spandrel  an-lu-s  in  the  haun-hes  prodnc..  a 
ight  and  arlisti.'  app..arance,  bul  th.n-  are  n..t  pra- 
tu^a bl..  tor  Hat  arch,>s. 

Spandrel  walls  may  be  built  c;  ut  as  curtains  t. 
obscure  the  op.Mi  chamb.-r  fran.ing,  or  as  retaini.r^ 
Avails  to  support  ..irth  filling.  As  retaining  walls 
thoy  may  be  built  .Mther  as  s.,lid  gravity  walls,  or 
as  lighter  r.-infonvd  walls  witi,  .-ounteWorts  In 
nnx  .vase  it  is  b.-tter  that  the  centers  be  re,nov...l 
JH.d  h..  arch  alhuvd  t..  settle  before  building  the 
spandrel  walls. 


Piers  and  Abutinea' 

On  the  stal)ility  of  the  f.»undatif.  .. 
of    the    whole    sup.-rstru.-tu.c    d.^pends.      Th.    „„-. , 
and   abutments   include   all   of   the   structure   from 


the  strength 
e    piers 


^; i^/S9v:^J?jsi)W,  .vivf *«,*£* :i-,<«i. 


^<:i.^ 


•.a  ■  -it^■.•"  -^i 


REINFORCED    COX  CRETE    ARCH    BRIDGES.    149 

tlK>  grouiul  up  to  the  point  of  rupture.  The  totiil 
Hii<rle  iru  hided  between  normals  to  the  points  of 
i-upture.  never  exeeeds  120  dejjrees  and  is  usually 
from  DO  to  no  dcrrrees.  the  real  theory  of  arehes 
api)lying  only  to  material  between  these  limits.  The 
part  below  the  points  of  rupture  must  be  designed 
in  eonneetion  with  the  substructure. 

The  neatest  eeonomy  in  the  design  of  abutments 
is  secured  by  using  low  springs.  If  higher  springs 
:ire  desired,  they  eau  be  secured  by  false  side  walls 
i!s  explained  and  illustrated  in  Part  I.  Great  sav- 
ing can  l)e  effected  in  high  abutments  by  coring 
out  the  rear  and  transferring  the  thrust  to  the 
soil  through  vertical  walls  bearing  on  a  foundation 
slab  of  leinforeed  concrete.  Abutment  wings  may 
I)e  l)uilt  as  cantilevers  from  the  arch,  extending 
into  the  embankment  only  far  enough  to  hold  the 
slope.  They  contain  nuu-h  less  masonry  than  the 
old  style  of  gravity  retaining  wing  walls.  Cantilever 
wing  walls  should  be  tied  together  with  rods  be- 
neath the  roadway,  to  resist  the  outward  thrust 
of  filling.  Thi.s  method  Avas  adopted  in  the  Topeka 
l)ridge. 

The  recent  failure  of  the  Peoria  bridge  over  the 
Illinois  River,  has  called  attention  to  the  need  of 
having  absolutely  secure  foundations.  The  Peoria 
bridge  was  destroyed,  not  beeause  of  any  lack  in 
the  design  of  the  sui)erstructure,  but  beeause  of  the 
undermining  of  its  foundations. 

Flaring  gra\ity  wing  walls  are  more  economical 
than  straight    ones   of    the  same   type   and  better 


k 


1 


1 


s 


j  I 


n\ 


I 


j  ii 


!fii 


^ 


150       COXCRETE   BRIDGES  AXD   CULVERTS. 

direct   water   to   the   opening,    but   straight    wings 
usually  present  a  better  appearance. 

River  piers  require  eut-waters  at  the  upper  end 
which  should  be  capped  with  stone  or  steel,  well 
anchored  into  the  masonry. 

Some  bridge  piers  have  been  given  a  different 
batter  on  the  two  sides  for  resisting  the  une.pial 
thrust  on  the  sides  from  spans  of  different  lengths 
The  piers  must  have  sufficient  thickness  to  resist 
the  uneven  thrust  caused  by  full  live  loading  on 
one  span  and  no  live  load  on  the  other.  Piers  must 
bo  designed,  not  by  empirical  rule,  but  accordin-' 
to  the  stresses  that  they  actually  have  to  resist 

The  presence  of  reinforcing  rods  for  resisting 
temperature  stresses  in  piers,  is  desirable  thou-h 
not  necessary.  Piers  are  usually  well  protected 
from  the  direct  rays  of  the  sun,  and  rods  are  more 
usetul  to  unite  the  mass  into  a  solid  monolith  than 
for  resisting  temperature  stresses. 

The  design  of  piers  for  reinforced  concrete 
bridges  does  not  differ  greatly  from  the  design  of 
piers  for  masonry  bridges,  and  most  of  the  discus- 
sion of  this  subject  for  Concrete  Bridges,  applies 
equally  here. 

Cost  of  Reinforced  Concrete  Bridges. 

There  are  numerous  considerations  that  affect 
the  cost  of  reinforced  concrete  bridges,  among  which 
are  the  nature  of  the  soil,  the  nearness  or  accessi- 
odity  of  materials,  presence  or  absence  uf  .switch- 
ing facilities,  the  design  of  the  bridge  whether  solid 
tilled  or  open   spandrel,   the  height,   width,   finish, 


RFIXFORCED    COXCRP.TP.    ARCH    BRIDGES.    151 

|>Hvin|yr,  wiiifrs.  otc.  TIm'v  will,  however,  rarely  if 
-vcr  cost  iii(»ri'  I  hail  hridjrcs  of  solid  concrete.  An 
•  •rijriiial  formula  for  the  cost  of  solid  concrete 
l»rid^'cs  has  l)een  driven  in  Part  I.  but  for  -onveniencc 
it  is  repeated  here.     It  is  as  follows:— 

HW 


C-F 


100 


Where  C  is  the  cost   of  the  bridge  in  dollars  per 

s(iuare  foot  of  roadway, 
W.  the  total  width  of  deck  'n  feet, 
II.  the  height  of  deck  above  valley  or  river  bottom, 

and 

!•'.  a  variable  factor  the  value  of  which  is  as  given 
Ix'lo'v, 

The  function  IIW,  or  the  product  of  height  by 
width,  is  the  cross-sectional  area,  and  may 
be  represented  by  the  letter  A.  Factors  F. 
it  re  for  bridges  with  solid  slab  arches,  while 
factors  F'  are  for  bridges  with  partial  slabs, 
like  the  Walnut  Lane  bridge  at  Philadelphia, 
or  the  Rocky  Kiver  bridge  at  Cleveland. 

Values  of  Factors  F,  and  F'. 

When  A  is     200.  then  F  is  l.T) 
500,  ••  1.0 

1000,        '•         .nr) 

1500.  ••  .ts 

2000,  ••  Al 

2500,  •  .;{0 

3000,  ••  .:J2 

3500,  ••  .285 


A 


' 


ji 


jij 


:i 


:H 


« 

« 


.224 

Mo 

.200 

.lU 

.ISO 

.<J8 

.104 

.<J2 

.152 

.91 

.141 

.S8 

.183 

.86 

.125 

.85 

l.'»2        CONCRETE   BRIDGES  AXD   CULVERTS. 

When  A  is  4000,  tlu'u  F  is  .202  uiul  F'  is  .0« 

50(M), 

r.(M)(>, 

7000, 

8000, 

IM)00, 
10000, 
1 1000, 
12000, 

This  fonimla  uill  give  costs  that  should  rarely  if 
ever  bo  exceeded,  (ienerally.  however,  eeonoiii- 
ieally  desipied  reinforced  concrete  bridges  shouhl 
c(.st  from  2."»9^  to  oO'/,  less  than  the  costs  given  by 
the  formula  for  bridges  in  solid  concrete.  In  a  few 
cases,  the  cost  of  bridges  in  reinforced  concrete 
liave  exceeded  tliat  given  by  the  formula,  but  these 
eases  are  rare.  Where  the  height  (h>es  not  exceed 
IT)  to  20  feet,  the  cost  will  usuallv  -.wy  from  .$2.00 
to  .$4.00  per  s<iuare  foot  of  lioor  surface,  while  for 
greater  heights  it  may  be  twice  these  amounts. 

The  total  cost,  as  well  as  the  cost  per  square  foot 
i»f  deck  for  a  miscellaneous  lot  of  reinforced  con- 
crete bridges  is  given  in  Table  Xo.  II.  The  square 
foot  cost  is  based  upon  the  total  length  of  bridge 
over  parapets  or  foundations,  and  not  upon  the 
length  of  opening.  If  based  on  the  latter  length, 
the  costs  per  sipiare  foot  would  then  be  greater. 

The  cost  of  IS  concrete  areh  highway  bridges, 
biiilt  by  the  city  of  I'hiladelphia,  is  reported  in 
Engineering  Record  January  23,  1909.  The  report 
states  that  the  bridges  Avere  mostly  single  si)an  with 


REIM-ORCEl)    CO.VC'i :/..'/•    AUCIl   BRIDGES.    153 

oi'nanii'iilal  balustrade,  washed  ^'ranolithic  surfaeos 
and  i)av('d  decks.  The  costs  based  upon  the  total 
length  of  bridire  vary  from  $1.7:?  to  $7.;5!)  per  s(puire 
loot,  or  ati  {"  -re  of  if;:!..')!)  per  s(|uare  foot,  while 
the  costs  ));•  .ipon  th.-  width  multiplied  l)y  the 
dear  length  .>f  pening  vary  from  $"?.1()  to  .t!).74,  or 
an  average  of  $0.2.")  per  s(piare  foot.  The  total  cost 
based  upon  tlu^  yardage  <>f  concrete  in  the  structure 
varies  from  .tS..')0  to  $11.2.1  per  cubic  yard.  The 
report  stales  further  that  if  large  spalls  or  stones 
were  embedded  in  the  concrete  1o  save  cement  and 
mixing,  the  cost  would  then  be  i-ednced  bv  abojit 
207; . 

("omj)ared  with  steel,  reinforced  concrete  bridges 
usually  cost  about  the  same  as  steel  bridges  with 
solid  tloors.  The  report  referred  to  above  states 
that  those  built  in  Philadelphia  i)roved  to  be  cheaper 
in  fir.st  cost  than  plate  girder  bridges  by  about 
2.")^,  but  if  maintermnce  expense  is  considered,  the 
saving  is  still  greater. 

Comparative  estimates  for  the  Memorial  P.ridge 
at  AYashington.  one  design  for  which  is  given  in  the 
frontispiece,  showed  that  the  reinforced  conerete 
designs  cost  45^  more  than  corresponding  designs 
in  steel. 

A  bridge  over  the  Hudson  River  at  Sandv  Hill. 
X.  Y.,  consisting  of  L")  ribbed  arch  spans  of  GO  feet 
each,  cost  only  $2.30  per  scfuare  fo(>t  and  a  steel 
i»ridge  for  the  same  loads  would  have  cost  as  much. 

Bids  received  for  a  bridge  over  the  ]\lississipi)i 
River  at  Fort  Snelling  Minn.,  consisting  of  two  arch 


ii 


mm 


! 


j 


13  ' 


I '. 


154        COXCRETll   BRIDGES  AND   CULVERTS. 

spans  ;{50  feet  in  length  each,  showed  that  the 
bridge  could  l)e  l)uilt  in  either  steel  or  reinforeetl 
concrete  at  about  the  same  cost. 

A  concrete  design  for  the  Richmond  trestle  shown 
in  Figure  40  is  reported  to  have  been  accepted  in 
I-reference  to  steel,  simply  because  it  was  the 
cheaper. 

Estimating. 

It  is  customary  to  estimate  the  total  cost  of  tioor 
slabs,  including  concrete,   metal  reinforcement  and 
forms,  at  2.")  cent  •  per  square  foot  of  floor  for  the 
slal)  only.    This  figure  is  nuide  up  as  follows-— 
concrete,    r.    inches    ,,,,,, 

woodforms:::::::::::::::::::::::::::::::::;::j-;g 

Total    o-  „„  » 

2o  cents 

The  cost  of  forms  varies  considerably,  and  for 
iloor  slabs  may  cost  from  8  to  20  cents  per  square 
foot  of  floor.  If  the  slal)s  are  estimated  separately, 
then  it  is  necessary  to  estimate  also  the  cost  of 
floor  beams  and  spandrel  cohunns.  It  is  u.sual  to 
estimate  the  cost  of  forms  for  beams  and  columns 
of  ordinary  size,  not  exceeding  about  one  and  a 
liiilf  foot  in  cro.ss-section,  at  50  rents  per  lineal 
foot.  To  this  must  l)e  added  the  cost  of  the  con- 
cr.-le  and  steel  in  the  member.  The  total  cost  per 
lineal  foot  of  girder  or  columns  would  then  be  as 
follows : — 

Concrete  1  cu.  ;V  t nz 

Sterol  f ?  <^ents 

Forms  ...'.'.'..'. l^  ^^"'^ 

oy  cents 

Total  71 

90  cents 


'^^miM:mm^ 


:UiifK:«d^Maij 


<V. 


REI.\  FORCED   COX  CRETE    ARCH    BRIDGES.    155 


TABLE  II 

APPROXIMATE  ESTIMATING  PRICES 


Price  delivered. 


Karth  filling ' 

Kxcavatintt,  ordinary ' 

under  water  (including  cost 

of  cofferdam) I 

Wood  piliiiR I 

Sheet  piling ' 

Concrete  pMini; ' 

Concrete  in  foundations '■ 

in  arc-h  rincs ■ 

includins  steel  reinforcement .  .    ' 

Concrete   imludine   steel   reinforcement 

and  centers ' 

Steel  reinforcement,  riveted  worii |    

rods,  plain  ' 

patented  rods ' 

Brick,  common !*ti  OOtoSlO  OOper  M. 


Price  in  Place. 


"    face. 

"    moulded 

"    enameled 

Concrete  blocks,  10  inches  thick 

.Sand 

(Iravel 

Cement,  Portland 

non-staining 

Crushed  limestone 

granite  

Bedford  limestone 

Cartilage  limestone 

Kasota  or  .\Iankato  stone 

(iranite 

Bedford  ashlar  facing,  4  to  S  inches  thick. 

Bedford  stone  carving  

Concrete  floor  siaba  i  concrete,  steel,  forms  i 
Concrete  girders  and  columns  (concrete, 

steel  and  forms) 

Concrete  columns,  spiral  wound 


30  00  "    " 
50.00  "    •■ 
70.00  "    ■■ 
.25  cu.  ft. 
.75  to  1.25  "    yd. 
1.25  "     " 
1.35  per  barrel 
3.25   " 
1.20  per  yd. 
3.00to3.50   "    " 
1.30  per  ft. 
2,00   "    " 
2.50  "    " 
2.50to3.00  "    " 


10.50  to  SI. 00  per  yd. 
.SOcu.  ft. 

4.00  cu.  ft. 

.351in.  ft. 

40.00  per  M. 

1.25  per  ft. 

6.00  •'   yd. 

8.00  "    " 
12.00  '•    '• 

18.00  "  " 
70.00  per  ton 
30.00  "  " 
50.00  "  " 
20.00  per  M. 
45.00  '•  " 
70.00  "  " 
100.00  "  " 
.SOcu.  ft. 


1.60  per  ft. 
2.30  "  " 
2.80  "  " 
3  30  "  " 
1.00  sq.ft. 
4.00  "  " 
.25  "    " 

l.OOlin.ft. 
1.70  "    '• 


u 


156        COXCRETli   BRUX.l.S   .\\l>   (II.IHRTS. 

TABLE  II  -Continued 

APPROXIMATE  ESTIMATING  PRICES 


\  I  ' 


BriilgF  pavftnents,  wood  block. . 
"  "  Krani)litliic  »!»lk^.  . 

brick 

"  "  asphalt 

"  "  stone  block. 

"  "  uranitp  blork. 

Railitie,  three  linos  pipe 

"      plaiti  iron  lattice 

"      fancy  iron  lattice 

"      artificial  stone    

Balusters,  turned  Rciiford  stone 

Hand  rail  and  base  rail. 

Stone  coping     

Intermediate  rail  iwsta 

End  newels 

Limp  posts       

Trolley  fxJes  

Lumber  in  co!Tenlani.< 

"      "    arch  centers 

"      "    forms 

Beam  and  column  form.s 
Metal  lath  and  pla.'iter,  int(  rior 

'         "         cMcriiir  . 

Expanded  metal  No.  10,  4-in(li  mesh. . 

•■    li?ht 

Nails  and  spikes 

Tar  pap'r 

Torh  Bros,  waterproof  paint,  No.  10.  . 
Bay  i'tate  coating  (for  concrete  surfaces) 
two  "oats ' 


$22.0t> 


O.'ijpcr  sq.ft. 
.02     "       " 


03  per  lb. 
005persq.  ft. 
125     "pal. 

.02      '•  s().  ft. 


RElXl-URCr.I)    COXCNl-.Tl-      IRCff    BKIDCI-.S.    1S7 


If  tlie  girder  or  column  is  larger  than  12  inches 
si(uare,  the  cost  of  the  concrete  will  then  increase 
in  proportion  to  its  area. 

In  making  up  a  tender  on  a  prospective  contract, 

it  is  necessary  that  all  items  of  expense  he  included 

and  provided  for.    Some  of  the  extra  exj)ense  items, 

that  are  not  inckuled  in  the  regular  estimate,  are 

as  follows : — 

Sui>erlntendent. 
Foreman. 
Timekeeper. 
Traveling  Expenses. 

Bond.     Cost  is  1   per  rent,  on  amount  of  bond,  which  is 
usually  25  per  cent,  of  contract. 
Telephones. 
Watchmen. 
Fire  Insurance. 

Liability.    Cost  is  2^  to  3 A  per  cent  of  amount  of  pay  roll. 
Permit  and  License. 
Water. 

Setting  <uit  survey. 
Rent  of,  or  depreciation  on  plant. 
Office  and  Storage  sheds. 
Material  tests. 
Models. 
SigHiil  lights. 
Pumi)ing  and  Baling. 
Refilling  and  Leveling. 
Shoring. 

Removing  Rubbish. 
Incidentals. 
Surfacing. 

These  items  must  be  provided  for  and  the  amount 
of  profit  desired  added  to  the  total. 

The  appi-  ximate  estimating  prices  given  above, 
should  be  changed  to  .suit  local  conditions  and  the 
varying  slate  of  the  market.  Prices  of  nuiterial  and 
labor  change  according  to  location  and  time,  and 
prices  that  are  suitable  in  the  East  may  not  hold 


w.m^ 


i 

i 


'I: 


!! 


I' 


i'pi! 


158 


coxcuini-.  HRinci-.s  .ixn  i(  i.niRTS 


for  work  in  lli(.  W.-st  or  S„utli.  The  j;n-at.-st  ran- 
is  iKMM'ssiiry  in  .•stiniatint?  the  fonn-lations.  I'or  tho 
pari  fliat  is  nns.'.-M  is  imc-rtain.  If  is  w.-ll  to  niak.' 
unit  pric's  for  a  <rrcat.T  or  l.ss  amount  ..f  founda- 
tions than  is  slionii  on  the  plans,  for  fre(iut'ntly 
more  is  rc()nii<'<l  tlian  is  anli.-ipat.d. 

Table  of  Approximate  Quantities. 

The  f(»ll(nvin,<r  lahh'  </nvs  the  approximate  ,,uan- 
titics  in  IJcinforcd  (  oncn'tc  Ardi  Ili^'liway  Hri.lf^.'s 
for  clear  spans  varyin','  from  L»()  to  150  fwt,  an.I  a 
••har  width  of  roadway  of  l(i  feet. 

They  have  solid  earth  filled  spandrels  witli  rein- 
forced eonereto  side  refainin«,'  walls  and  the  rise  of 
arch  is  one-tenth  Die  span. 

They  are  proportioned  for  a  live  load  of  200 
pounds  {..>r  square  foot  on  the  »  .adway.  The  quan- 
tities of  material  in  the  abutmen  ^  are  only  approx- 
imate. 

_I^^"^  OF  APPROXIMA  re  QUANTITIES. 


'  livir  Sp.'i 

III 

tVct. 

20 

;«) 

4(1 
.">() 
00 
70 
80 

go 

100 
110 
120 
130 
140 
150 


('ri)Hii 
Tlil<kiicHs 
rn  Iticlu's 

•) 
11 
i:i 
i:. 

16.5 

is 

19 
21 
22 
24 
26 
-.8 
30 
32 


■•■./.».'  .t.-.< 


t.l-jl. 


i^.l 


Rn/.xPi    cm  ((KWh'nTE  arch  URinc.r.s.  i-'.!> 

Por^mac  Memorial  Bridge  Design. 

This   is  (    ic   of  several  »l('si«;ns  sjihiiiittcd   to  tin' 
I'liited   St}i(   >;   (ioveniiiieiit    ill   tlu'  yciii"   l!K)()  for  ii 
;ii'(i|»ose«l  iiieiMoriiil  l»ri<lf;e  aei-oss  the  I'utomne  UivtT 
;it  \Viishiii«:l(ni      ft  liais  a  clear  width  of  ()<>  feet,  con- 
sist iii};  (»r  a  4«i-t'o()t   roadway  aMd  two  lO-i'oot   sith- 
wulks.     The    tnial    h-nptii    of   open    hridsrt'    is   :i,400 
feet.      It    has   one   deck   ami    no    provision    for   car 
tracks.      There    are    six    sejrniental    reinforced    con- 
crete  arch   spans   of   1!I2    feet    clear   len^'th    and   20 
fet  t    rise,    with    •');;    feet    clearance    nndei'neath.      A 
donl)le  leaf  trunnion  bascuh*  draw  span  is  centrally 
located  hi  t ween  the  arch  spans,  having  a  elear  open- 
ing of  1.")!)   feet   and   a   distance  between   centers  of 
trnnnions  of  170  feet.     The   Washinf^ton   approaeh 
consists  of  twehe  senucircular  reinforced  concrete 
arch  spans  of  GO  feet  elear  length,  and  ."i.'jO  feet  of 
end)ankiuent.  wliile  the  Arlington  approach  has  fif- 
teen similar  sji,  iis  and   I.IJ.IO  feet   of  enihanknient. 
The   entire    e.xi.iior   surface    is   shown    faced   with 
granite     '1  i;  •  fiu-e  rings  for  main  spans  are  T)  feet  (i 
inches  di    i    .ii  tlie  crown  and  9  feet  0  inches  at  th(! 
.springs.      Each    main    span    has    five    eonerete-steel 
arch  ribs  .U)  inches  ileep  at  the  crown  and  7  feet  )} 
inches  at   the   springs,  supporting  a  system   of  in- 
terior steel  columns  carrying  the  tioor  beams.    Span- 
drel curtain   walls  with  expansion  joints  rest  upon 
the   arch   rings   and   are   faced   with   granite.     The 
design    shows    asphalt    road   and    granolithic    walks 
laid  on  concrete  floor  arches  between  the  steel  floor 
beams.     The  estinmted  cost  is  $3,080,000.     William 
II.  Burr,  engineer;  E.  P.  Casey,  architect. 


i 

I' 


In. 

it 


:£ 
a 


:k 


RISIX  FORCED   COXCRETE   ARC  I    BRIDGES.    161 

Jamestown  Exposition  Bridge. 

This  l)ri(lov  was  built  in  1007  by  the  rnited  States 
(ioyerninent  to  conneet  the  outer  ends  of  two  j)i('i-s. 
It  is  of  reinforeed  eonerete  and  has  a  eh-ar  span 
of  lol  feet,  with  a  20-foot  rise.  It  is  36  feet  wide 
and  is  for  pedestrians  only.  The  aseent  of  the  road- 
way is  made  l)y  means  of  a  series  of  steps  and  land- 
ings. It  has  two  reinforeed  eonerete  areh  ribs  ear- 
rying  the  roachvay  on  four  lonjjitudinal  walls.  The 
abutments  are  eored  out  and  rest  on  piles.  Then- 
are  26  phunb  piles  and  12(i  l)atter  piles  under  eaeh 
al)utmenf.  It  was  designed  and  built  by  the  Seo- 
lield  Company  of  Philadelphia. 

Franklin  Bridge,  Forest  Park,  St.  Louis. 

^^)rest  Park  has  a  very  interesting  eonerete 
bridge  of  the  Melaii  type,  known  as  Franklin 
Uridge.  It  has  a  sj)an  of  60  feet,  a  total  width  of 
3:?  feet,  and  a  rise  of  If)  feet.  It  has  a  24-foot  road- 
way and  one  6-fo()t  sidewalk,  with  a  total  length  of 
!>2  feet.  The  areh  ring  is  three-eentered  and  varies 
in  thiekness  from  11  inches  at  the  erown  to  ^O 
inehes  at  the  springs.  At  the  four  corners  there 
are  ornamental  iron  lampposts  not  shown  in  the 
illuslralion.  lis  total  cost  was  .+r).(;00.  The  Geisel 
Construction  Company  were  the  contractors  and 
John  Dean,  Engineer  for  the  Park  Department. 

Jefferson  Street  Bridge,  South  Bend,  Ind. 

The  bridge  across  the  St.  Joseph  River  with 
tour  elliptical  arches  of  110-foot  si)an  each.  The 
l>icrs  are   cpiite   elaborate   in  design,  being  carried 


\ii 


'  I 


4 


7    I 


a  t- 


e^   * 


iti2 


REIXFORCED    COXCRETE   ARCH    BLIDGES.    I6;i 


V. 


up  to  support  retreats  at  the  sidewalk,  and  there 
IS  a  heavy  nioidded  eorni.-e  suniidunted  with  an 
artistie  railing.  At  the  ends  are  steps  leading  down 
from  the  roadway  to  the  river.  The  lines  of  tlie 
structure  are  true  to  a  design  in  concrete,  and  tliere 
has  been  no  elfort  made  to  imitate  stone.  The 
Concrete  Steel  Engineering  Company  of  Xew  Yoi-k, 
were  engineers,  and  James  0.  Ileyworth  of  Chi- 
t-ago. contractor.  A.  J.  Ilannnond,  City  Engineer 
of  South  Bend. 

Gary,  Indiana,  Bridge. 

Gary  is  the  home  of  the  new  steel  companies 
where  an  entirely  new  town  is  being  built.  The 
l)ridge  shoAvn  is  quite  ornamental,  and  illustrates 
some  possibilities  for  single  spans.  The  face  of 
arch  and  sj)anrlrcis  are  i)ineled.  and  the  wings  are 
curved  to  facilitate  approach.  At  either  end  of  the 
arch  are  pilasters  extending  up  to  the  cornice  and 
forming  in  the  balustrade,  pedestals  for  future  lamp 
standards.  The  bridge  spans  the  CaluuK  1  TJivcr 
and  was  built  in  1908  by  Rudolph  S.  Bknne  ^^-  Co.. 
<<f  Chicago. 

Como  Park  Foot  Bridge,  St    Paul. 

The  Como  i'aik  liridge  w.is  ])uilt  in  the  year 
1003  for  the  Twin  City  Rapid  Transit  Conipany  to 
carry  traffic  entering  Conio  Park,  over  t!i.  tracks 
'»f  the  street  railway  company.  The  bridge  has  a 
clear  span  of  .30  fed.  a  roadway  oi  l.")  feet  and  is 
built  on  the  ?,lelan  system  As  a  large  luunber  of 
passengers    leave    the    cars    at    the    bridge,    it    Avas 


n 


t  I 


\ii 


u 


lli 


i-ii'-ff-k 


b,    ^ 


w 


< 
/: 


SIC   ^ 


ue 


i  ' 


•(1 


!  '    i 


1    f 


t    ( 


I    J 


!    I 


I 


I    f 

ii 


"  »  !: 


HI 
lb 

1| 


166 


COXCRETI-:    BRIIH;i,s   AM)   crLnmTS. 


<l.'s.rable  that  tho  slruct.nv  sl,u„M  lunc  a  n.-at  an- 
poaraneo.  T„  order  to  avoid  for,,,  ,„ark.s  on  the 
exposed  surfaces  the  forms  wore  covered  with  metal 
iath  and  neatly  plastered  hefor,-  plneing  the  eon- 
erete.  The  length  between  centers  of  abutment 
piers  ,s  8:}  feet,  and  the  total  wi.lth  of  arch  is  17 
feet  2  niches.  It  has  a  rise  <,f  12  f,.,.t  fi  im-hes.  and 
IS  10  inches  thick  at  the  -rown.  The  length  of  span 
openings  over  spandrels  and  abutments  is  12  feet 
and  the  thickness  of  the  skewback  piers  is  2  feet' 
There  are  five  latticed  steel  Melan  arch  ribs  in  the 
concrete.  It  was  built  by  >Villia„.  S.  Hewitt  &  Co 
of  Muineapolis.  George  L.  Wilson  was  consulting 
engineer.  ° 

Boulder-Paced  Bridge,  Washington. 

In  a  park  at  Washington.  1).  (<..  there  is  a  boulder- 
faced  arch  of  rustic  design  ,na<le  to  confor,n  with 
the  surr(,undings.  It  has  a  span  of  SO  feet  a  rise 
of  1.)  leet.  and  a  clear  widil,  of  roa.lwav  between 
parapets  of  2:3  feet.  The  entire  arch  ring'is  built  of 
concrete,  but  the  soffit  is  darkened  witli  lampblack 
to  harinon.ze  with  the  boulder  facing.  The  boulders 
ot  the  arch  ring  extend  down  below  the  sotlit  .sev- 
eral indies,   and   partly  obscure  the  concrete  arch 

W    T    n     T  '!"'"   '"  ^-'^'^    "*  ^  '''''  ^f  -^17,500. 
vV.  J.  Douglas,  Engineer. 

Grand  Rapids  Arch  Bridge. 

This   is   a    good   exa„,ple   of  the    best   American 
practice  ,n  reinforced  concrete  arch  bridge  design 
It  has  five  spans,  the  center  on.  l,,ing  S7  tVet    th.^ 


^ 


REINFORCED   COXCRETE    ARCH   BRIDGES.    169 

two  adjoining  ones  83  feet,  and  the  two  end  spans 
79  feet.  It  has  a  clear  width  between  railings  of 
64  feet.  The  piers  have  moulded  concrete  cornices 
at  the  springs,  and  there  is  a  continuous  cornice 
.supported  on  brackets  at  the  floor  level.  There 
iu-e  retreats  in  the  .sidewalk  above  the  piers,  and 
•A  heavy  open  balustrade  with  seven  heavy  railing 
posts  in  each  span.  It  was  designed  by  William  F. 
Tubesing  under  the  direction  of  L.  W,  Anderson, 
rity  Engineer,  and  was  built  in  1904  by  J.  P. 
Ivusehe,  contractor,  of  Grand  Rapids,  ilich. 

Bridge  at  Venice,  California. 

At  the  little  town  of  Venice  in  loiver  ^VV!  rnia, 
laid  out  with  numerous  canals  in  imitnt-  -;;  of  Ital- 
ian Venice,  are  a  number  of  bridges  mostly  built 
of  concrete  with  features  of  unusual  design.  The 
town  being  on  the  sea  coast,  in  a  region  where 
flowers  and  foliage  abound,  has  probably  suggested 
the  ornamentation.  The  faces  of  the  arch  are  elab- 
orately decorated  with  festoons,  and  on  the  ends  of 
the  balustrade  are  grotes(iue  figures  of  sea  animals 
in  concrete,  the  size  of  which  may  be  estimated  by 
comparison  with  the  people  on  the  bridge. 

Garfield  Park  Bridge,  Chicago. 

ITae  illustration  shows  an  attractive  park  bridge 
I'uili  in  the  year  1S93  in  (jarfield  Park.  The  open 
l)alustradH  with  the  heavy  circular  piers  together 
with  the  combination  of  rough  and  smooth  finis'ii 
unite  to  produce  a  pleasing  appearance.  'Medal- 
lions on  the  piers  have  monograms  with  thf--  park 


II 


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MICROCOPY    RESOLUTION    TEST  CHART 

(ANSI  and  ISO  TEST  CHART  No.  2) 


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^     APPLIED  IIVMGE 


1653    East    Wain    Slreet 

Rcchester,    Ne«    Yorn         14609       USA 

(716)    482  -  0300  -  Phone 

(7!6)    288  -  5989  -  Fox 


REIXPORCnn    COXCRP.TP.    ARCH   BRIDGES.    173 


c 
o 
< 
o 

s: 
u 

.  o 
M  a 

^    PS 

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< 


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M 


iiiilials,  and  tlie  spaiidrt'ls  arc  paiu'lcd.  The  balus- 
trade posts  are  mounted  with  ornamental  urns.  The 
design  is  one  Avhieh  can  well  1)e  reproduced  in  con- 
crete with  either  cut  stone  or  moulded  concrete 
facing. 

Stein- Teuf en  Bridge,  Switzerland. 

The  longest  concrete;  arcli  span  completed  is  at 
Stein,  Swit/ciland.  Its  total  length  is  5r)0  feet,  and 
the  roadway,  ;>2  feet  wide,  is  210  feet  above  the 
Sitter  River.  The  central  span  is  2.")!)  feet,  with  two 
approach  spans  '-V^^'-^  feet  long  at  the  Teufen  end, 
and  four  at  the  otlier  end.  The  central  piers  are 
ticavily  reinforced  to  resist  unbalanced  thrusts  from 
the  adjoining  arches.  The  main  arch  rings  are  21  ^j 
feet  wide  and  4  feet  t'  ick  at  the  crown,  increasing 
to  the  springs,  raid  reinforced  with  lVs-i"t'h  round 
bars  from  10  to  \S  inches  apart.  It  has  a  Telford 
pavement  and  2-foot  walks  on  ct)nerete  slabs  sup- 
ported on  stringers  and  spandrel  columns.  The  con- 
crete balustrade  has  openings  '.\  feet  wide,  guarded 
Avith  embeilded  bars.  It  was  designed  by  Professor 
-Alorsch,  and  cost  $80,000. 


ih 


1 1 


:t 


■  i.\> 


m 


174        COX  CRETE   BRIDGES  AXD   CULVERTS. 

TABLt  III 

LIST  OF  REINFORCED  CONCRETE  BRIDGES 


ri.Aci:, 


C»V.T. 


B 


X. 


J    Stein,  .Switzerland sitter  Kivcr  , 

I-  oKanis-Kronstatlt,  Hunuary 

T     Decize,  i-rance ' 

>    I'yrimont,  Trance 


■r.        ^ 

_•  '       c 


-=■ 

s 

s 

V 

.c 

% 

a 

TT 

— 

H 

?: 

K  ; 





i 

Loire  River 

Ulione  Kiver. . 


1  I  259 
6  33.5 

...i  197 

2  184 
2  177 


Bornjida.  Italy 

C'hatellerault,  France. . 

Painesville,  Ohio 


9 
10 
11'   ^ 

12    Jamo.stiiwn,  Virginia. 

I.'i    I'layadel  Kev,  tal 

Wakenian,  Ohid 

Uiiul'  \Vaiiili()len,  .\iistria. .  . 

■Steyr,  .\ii.stria 

liranth  HrcHiJt  I'ark,  Newark 

To|)eka,  Kansas 


\  ienne  River   . . 
Grand  River 


14 

1.5 
Hi 
17 

IS 

19 
20 
21 
22 
2.i 
24; 
25' 
2ii 

r, 

2s 
29 
30' 

3i; 

32 
33  i 
34, 

35 

3li 

37,1 

■AS 

3.» 

4(1 

41 

42 

4.': 


\crmillion  River . 


Kansas  River. 


Route  WililcKK,  .Switzerland 

■ielliiwstiine  I'ark 

I'orto  l{i(0 

Lansini;,  M'chiiran 

Lake  I'ark,  .Milwaukee 

I'lirtucal 

Third  St.,  iMvlun,  Ohio 


.\vranelie.  i  ranre. .  . 
Hoiilevard,  St.  Paul. 
Circen  Island 


Vellow.stonc  River 

Jaea:|uas  Kiver..  . 


Orand  River 
Ravine. . . 
1  ena  River. 
.Miami  River 


.feffersun  St.,  South  Benii 

Knitricli.sville,  Ind 

Morris  St.,  Indianapolis.. 

I.aihaeh,  .Vu.^tria 

Huntincton,  Indiana.... 
Buda  Pesth.  .\ustria 


Canal  Dover,  Ohio 


.■^ia-ara  River  . 

St.  .loseph  River  . 
White  River.  .    . 


Danube  River 

Tus{-arawas  River . 


I  li 

i} 

!  2 

\   1 

'   2 

1 

'1! 

1  ! 
1  ■ 
1  i 

2  I 

2  I 

1  ! 

1 

1 

2 
1 
1 
5 
1 
2 
2 
2 
1 

i 

2 
4 
3 
5 
1 
2 
1 
2 
3 


175 
167 
164 
131 
160 
70 
151 
146 
145 
144 
139 
132 
125 
110 
97  5 
122 
120 
120 
100 
120 

lis 

114 

110  i 
100 
90 
80 
110 
110 
110 

100  ; 

110 
110 
90-110 
108  I 
104 
in.*!  ! 

96  I 
107  ' 


87 
15 

i.5' 

550  22 

"  1" 

....!.... 

....  34 
612  12 

21ti 

4.< 
14 

25 
16.7 

"»l  '•• 

15.7 
13.2 
71 

26" 

443  20 

401  68 

....'36 
205  19 
219  21 

1 

22 
90 

Sett. 

18 

33.5 

36 

8.5 
16.2 
18.9 
16.3 
14.6 
1 1  i 

165  19.7 
244  74 
693  40 

"  i" 

1(1  o 

19 
24 
32 

Sen. 

15 
12 
11.4 
23 
18 
14  4 
9  6 
11  3 

13  3 

14  3 
23.5 
40 
11.5 
10 


14.6 
14 
14  4 
9  5 
11  7 


12.8. 
160  17 
404  20 

**   *t 

. . . .  64 
214  54 
.  .  11.8 
710  12 


. ...  10.5 
222  40 
371  41 


43 

39 


25 

30 


3  I'. 


170  50 
240  16 

..._.  45 

.522'.55 


50 
16 


25  3C. 
21 


30 


REINFORCED    COS'CRETE    ARCH    BRIDGES.    175 

TABLE  III— Continued 

LIST  OF  REINFORCED  CONCRETE  BRIDGES 


4.'i 
14 


SeK. 


u 

S 

M 

I 

1! 

c 

1 

1 

0 

X 

■0 
c 

OQ 

6 

Kngineer. 

References. 

E.C.,  Eng..C  m. 
X..       "      Xews 
H..       "      Reccird 

i 

is 

1 

1  'll 

10 
8 

ISOU 

u. 

$80,000 

Morech 

X     \ua.  5.  '09 

1 

A 

1 

4 
5 

6 

7 

18 

H. 
H. 

H. 
H. 

1907 

*4 

190? 

$42,400 

Ue  Mollius 

N..  Apr.  2.  '08... 

Rib. 

$5.50 

?1 

?? 

1899 

4i 

1908 

1907 
1906 
1908 

35,000 

N.,  Apr.  10.  '02.. 

Rib. 

3.05 

8 
g 

1H 

S7 

R.  R. 

Leffler 

R.,  Apr.  24.  '09 

10 
11 
12 
13 
14 
15 
16 

54 



Scofield  Eng.  Co 

Rib. 
Rib. 
Rib. 
Rib. 

?4 

DePalo 

Watson 

N..  July  26,  '06. 
E.C.,  Feb.  24,  '09 

H. 
H. 
H. 
H. 
H. 

16,870 

3H. 
3H 

3.66 

n 

36 
36 
36 

'24' 
30 

1897 
1895 
1897 



84,000 
150,000 

Reynolds, 

Keepers  &  Thacher 

R.,  Aug.  12,   05. 

4.6,5 
5.40 

]7 

20 

it 

a 
,2 

R..  Apr.  16,  '98.. 
N..  Apr.    2   '96. 

18 
19 
20 
21 

19 

7    ...  .  ! 

1890 
1904 
1901 

190? 

H. 
H. 
H. 

H. 
H 

24    1 

59,440 

Crittenden 

N.,  Jan.  14.  '04 

•)•> 

2S 

*.?'♦ 

R.,  Aug.  3.  '01 . 

7.40 

?'< 

?l 

N.,  Aug.   1,  '01 . 
E.C.,  Mar.  17    '09 

24 

31.000 

25 

! 

1904 

Newton  Eng.  Co. 

R.,  Nov.  25,  '05 

Rib. 

26 

190l'E.  K. 

■'7 

26 

32 

1906 

H. 

1* 

184.000 

Turner 

R..  Mar.  4, '06.. 

4.18 

28 
?'t 

"  t 

..!.... 

cO 

•> 

31 

Rib. 

1? 

1909 
1900 

H. 
H. 

18.800 
102.070 

C..\.  P.Turner. 

R..  Apr.   3,  '09 
X.,  Dec.   6,  '00 

2.12 

6.60 

33 

4(1 

e.i'?* 

36 

34 

38 

R     Feb   Ifi    '01 

■?") 

.    E.  R. 

Hammond 

36 

1 

H. 
H. 
H. 
H. 
U. 



V 



38 

20 

"h" 

42 

12 

1901 
1907 
1900 

32,000 

Melan | 

N..  July  16.  '03 

3.77 

39 

21 



40 

20 

41 
42 
43 

24 

24 

lU 

12 

1905 

H. 

105,000 

Thacher R.,  Feb.   9,  '07 

?'=  !*¥.'"'-«;>•■    '' 


iT9B?r?^>- 


176        COXCRLTE   BlUDGLS   AXD   CULVERTS. 


i 


I 


ll 


^1 


(: 


W 


i 


'I 

[! 

'IN 


TABLE  III— Continued 

LIST  OF  REINFORCED  CONCRETE  BRIDGES 


E 

3 

H 

45 
46 
47 
48 
4U 
50 
51 

52 

53 

54 

55 

56! 

57 

58 

59 

60 

61 

62 

63 

64 

65 

66 

67 

68 

69, 

70: 

71 

72 

73 

74 

"I 

78' 

77, 

78' 
79 
80 
81 
82 


PLACK. 


Over. 


I  usi-arawas  Kivtr 
I  luster  Hay 


Canal  Dover,  Ohio 

Felham 

Draw  .Span 

Paterson   Xew  Jersey Passaie  River. 

"  ayne  ^t.,  Peru.  Indiana ...     i  A\  abash  Hiver  . 


Sixth  Ave.,  Dea  Moines,  Iowa       lies  Moint  > 


Stocl'^^rIdKe,  Mass. . 
Decatur,  iUinois 


Hoosatonic  River . 

l^anf^amon  River  . 

Yorkton,  Indiana. ....  ..   ' 

Cartersburg,  Indiana 

W  ashington  St.,  Dayton Miami  River  ..'.'.'. 


WateryiUe,  Ohio ::;;::  j  Maumee  River. 

Main  fetreet,  Dayton I  .Miami  River. 


Paterson,  >;ew  Jersey.' .' .         ,      Passaic  River.' 
Grand  Rapids,  .Mich Grand  River .  . 


Seeley  St.,  Broolilyn.' 
New  Goshen,  Ohio.  . . 

Sarajero,  Bosnia 

Decori!,,  Iowa 

\\'ashington,  D.  C. . , 


Prospect  .\venue 

MilJEclia 

Rock  Creek 


Soissons  France.   Aisne  River. 

tolfax  Ave.,  South  Bend 


Cedar  Rapids,  Iowa 

I'ollasky  California '.'.'.'.'.'.    Sanjoaquin   Kivor 

i^resno,  Galicia, .  I   . 


Hyde  Park-on-Hudaon.' .' .' .' .' .' ' .  j  Crum  Elbow  Creek 


1 

2 

2 

2 

12 

1 

o 

2 
2 
o 
1 
2 

5 
1 
2 
1 

3 
1 

8 
10 
1 
2 
1 


70 
lO.-i 

1)2 
108 
100 

9.5 

80 


100 

100 
100 
93 
95 
90 
90 
8B 
80 
74 

75-90 
88 
S3 
76 
63 
88 
87 
83 
79 
85 

83.5 
81 
81 
80 

80 
77 

75 

75 
75 
73 
75 


J 


10 
Hi  ,i 

12 
15 


13 


c 

•=  5  ^  C 

2  —  .^  > 

"c  :=  *S  ,      ^ 


522  55 

807  ..-.a 

360  40 

6St  ;-,o 


,23.9    36042.7 
120. 

124  7.5 

640  28    i 


10 
30 


11  ..  il8 
15.7:  21222 
115,  62054 

10    I    '■  r 

9.3     "  1" 

8     i     '•   " 

22-25  120016 

5}5t  56 


30 
30 

El.' 

20 

28 

!'.'•. 

(i 

24 

32 

3C. 

15 

60 

26 
30 

«» 

** 

45 

9.5   317  30 

49£  C4 


8 

II     I  "j- 

8.5  144,53 

8.2  494  16 

8    I  10;'S6 

9.7;  18726 
13t'27 


8 
7 

7 
11 


30  I  3  C. 


18 
30 


30545        30 


14.7 


....;42 

780;19.5 

257:... 

..    20 


18 
21 


5C. 
Seg. 


Seg. 
Seg. 


3C. 


5C. 


-J    w!m 


REINFORCED    CONCRETE   ARCH   BRIDGES.    177 

TABLE  III— Continued 

LIST  OF  REINFORCED  CONCRETE  BRIDGES 


El. 
3  C. 


3C. 


If. 


c 
o 


.a 

CO 


M 


Engineer. 


Reference*. 

C,  Cement 
N.,  Eng.  News 
R..     •'    Record 


l.i       lU     [18  J1905. 
24    Frame '  36   190b    H. 


Thaoher. . . . 
Lindenttul. 


R.,  Feb.   9,  '07. 
R.,  Oct.  31,  '08. 


28 
25 

21 

21 

9 
45  , 


21 
20 
11 
7 
17 
24 
20 


19 
27 
18 
12 
18 
17 

12 


16 

IS 


1« 


1      i  24  ,1907i   H. 
^     I    6  1 1905;   H. 

i    '   '    " 

"     ■  12  i    •'  :    " 

!  I  ! 
...1901    H. 

"  ^  I  i 
7    I    I  2S   1895  F.  B. 

1      '  12  1907  R.  R. 


l.i     10  I 

1.     lU 


1'4 


37,200    Wise. . .  . 
36,900    Luten. ... 


R.,  Mar.   7,  '08. 
X.,  Mar.  29,  '06 


C,  July,  '02. . 


1,475  I  Von  Empereer . 
117,000  i  Cunningham   .  . 


V,  Nov.  7,  '95 
N.,  Mar.  21,  '07 


.     1905    .. 
6   1907  E.  R 
3t)   VMa    H. 


0   1908  E.  R. 
.     1903    H. 


j  Luten. . 

Luten. .. 

122,000    Turner.. 


36  i  ;; 

3t)   1897 
30   1904 


i  8   1903 

'  18   1906: 

,  24   18971 

i  12   1906; 

\  33  :1901 


77,000 
140,000 


Walker. 
Turner. . 


Thaoher. . . . 
TubesinR.  . . 


.\.,  May  11, '05 


R..  Mar.   2.  '07 


R.,  Xvif,  8,  '03 
N.,  May  19.  '04 


N..  Mar.  16,  '99 
N.,  Dec.    1,  '04 


'1903  R.  R. 
,1901    H. 


21,803 
16,500 
17,500 


Fort.  .  .  . 
Murray. . 
Wunsch . 
Luten.  . . 
Douglas . 

Riboud. . 


N,  Deo.  31,  '03 
R.,  Mar.  30.  "07 


R.,  \u<r.  16,  '02 
.v.,  kMK.  14.  '02 


i  .36  '1906 

H    I   .  . .  1905 


1897i   H. 


» 


Rib. 
Rib. 


1.80 


1.58 
6.50 


3.60 


4  00 
4.30 


12.90 

4.65 
4.30 


4.95: 


• .  ••     ■  Marsh  Bridire  Co. 
4S,000  I  Li-'.iiard 


Conrrete  Steel  Co. 


R.,  Feb.  24.  '06 

3.15 

::::i:;;: 

44 

45 

46 
47 

48 
*i 
50 
51 

52 

53 
54 
55 
56 
67 
58 
59 
60 
61 
62 
63 
64 
65 
66 
67 
68 

6a 

70 
71 
72 
73 
74 
75 

76 
77 

78 
79 
80 
81 

(-2 


i 


178 


; 


i 


I  i 


»H 


si ; ! 

\  t 


'-\iU 


i   ii 
il 


coxcRinn  BRinGHs  axd  culverts. 
TABLE  III— Continued 

LIST  OF  REINFORCED  CONCRETE  BRIDGES 


near  Tcrre 


S3,  "Bin  Koiir 

I      Haute.   

S4|  Wabash  Indiana  ;:.;.'  Chariey'  Creek, 

N.)    Mission  Ave.,  Spokane. .  j  '      ^- 

m    Olive  .\ve.,  Spokane.  . 

S7    Meridian  St.,  Indianapolis. . 

KS    Illinois  St. 

S9    Northwestern  .\ve.,Indianapo| 

90  Derby,  t'onn 

91  Waterloo,  Iowa 


9? 
%i 
94 
95 
9fi 
97 
9S 
93 
100 
101 
102 
WA 
lO-l 
10.-) 
lOf) 
107 
108 
109 
110 
111 
112 
113 
114 
ll.i 

nr> 

117 

lis 

119 
120 
121 
122 


i^pokane  River. 
Fall  Creek 


Kdcr.  Park,  Cincinnati 

LoKan.sport,  Indiana 

-Austell,  Georeia 

Trinidad,  Colorado ' . ' . 

\\  abash,  Indiana 

Seventeenth  .St.,  Boulder,  Ci)l . 

lola,  Kansas 

I'orto  Hi™ 

Howlcvard  Brid-e,  Philadelphia 
.lack.sonville,  Florida.... 
Herkimer,  N.  Y 

Sandv  Hill.  N.  yV  ■.'■:'    ; 
Iranklin  Bridge,  St.  Louis... 

Lima,  Ohio 

Plainwell,  Michiian 

Maryl)or(>usth,  Queensland.  . .  . 

Como  Park,  St.  Paul 

AtlanticHi^hlands,  N.  J...  . 

(ilendoin,  Cal 

Fore,st  Park,  St.  Louis '.'. 

London,  Ohio 


FarkTrive. 
1 ine  t  reek. . 


Miners  Ford. . 
(iuaya  River. 


R.  R.  Trark-s 

W.  Canada  Creek 

Hud.son  River.  .  . . 
I  ark  Stream 


C'uftSt.,  Indianapolis 

Oconomowoe,  Wisron  in 

Columbia  Park,  Lafavette 

Interlaken  Bridse,  Minneapolis 
Plainfield,  Indiana 


Kalamazoo  Ri\er 

Mary  River 

Tracks 

firand  .Ave 

San  (labriil  Ri\er 
River  I  es  1  ercs  . 


1. 


Chicapi.C.  &  E.  L  Ry^ 


Trim  Creek. 


II 

:  3 

3 

!  7 

1 
2 
4 
2 
2 
I 
3 
3 
1 
11 

I? 

15 

I 

2 

7 
11 

1 

1 
IS 

1 
I 

2 
I 
I 
1 
1 
1 
2 
2 
1 


7.5 
7.i 
70 
9,5 
74 
74 
74 
72 
72 

70 
70 
70 
70 
70 
70 
70 
70 
69 
66 
66 
62 
60 
60 

59 

54 

50 

50 

50 

50 

45 

45 

40 

43 

42 

40 

38 

42 

39 
35 
38 


i 

-CI 

» 

t- 

Vi 

s|  6 

■~"~~  ~ 

18 

24(1 

32 

24 

Par 
^1- 

'2. 

5a5 

•■ifi  ■ 

26 

«  5 

284 

70 

18 

3C 

96 

284 

eo 

18 

3C. 

54 

7.2, 

1 

586 

46 

20 

C. 

10    1 

33 

r 

14 

163 

16 

1»  j 

20 

300 

26 

45  1 

5C. 

7 
18 
10  5 

9 

7 


201 
240 
89 
242 
270 


7  845 
14  755 
12 

8.5  1025 
15 

8 

8 


64 
32 
24 
14 
20 

52 


li    3  C. 
24  i  Par. 

13  i. 

14  i. 
20  I  3  C. 


35 


4 

12. 
11 


12 
6.2 
5.7 
8.5 
6.8 
4 


7.6 

7   2: 

6.51 


9233 

16l!l6 

446  23 

613;23 

8317 

. .  i25 

101926 

65  45 

150,16 

53 '20 

....|15 
56  6 
82  63 

216  16 


48 


30 

..... 

32-4C 

jSeB. 

24 

3C. 

18 

, 

22 

SeK. 

22 

SeK. 

C. 

22 

12 

11 

17 


s\ 


REIXVOKCED   COXCRETE   ARCH   BRIDGES.    179 

TABLE  III— Continued 

LIST  OF  REINFORCED  CONCRETE  BRIDGES 


I 
■f  i 

i 

N 

■7. 

I        ' 

^  1  i 

-=.  &   -^ 

1 

55.000 

54.400 
50,900 

54.000 



KnKincrr. 
Duane 

I 

References. 

K.C,  Eng.-Con. 

N..       ••      Nc«s 

,  R.,       "     Rccon 

1 

1 

1        1 

■I 

3  X  i 

.'     'r.r 

24      ,        H. 

1     ( 

83 

IS 

Hiltv 

Mclntyre 

RaUton 

Jcup 

Jcup 

Concrete  i*tecl  Co. . 

Concrete  Steel  Co. 

Von  EmperRer. .  . 
Lutcn 

X..  Dec.  6,  '07 

.\.,  Apr.ii.'Ol 
N..  Apr.  11,   01 

71 

H. 
H. 

14 
(* 

b6 

2.65  87 

2.90  S8 
J.9 

Ifi 
II) 

10"  I 
10"  1 

36   1900 
36  |1900 

E.C.,  Mar.  17,   07 
R..  Feb.  13.    04 
N'..  Oct.    3,    95 

(in 

14 

15 
14 

2'2X'i 
9"  I 

v: 

1', 

3x1 

i"   1902 

3e   1895 
12   1905 

..     2.00  91 

..     93 

94 

95 

40 
14 
IH 

12 

r; 

J4 
'.2 

1905  R.  v.. 
1905    H. 

Wells 

Hibbard 

Kahn 

National  RridceCo. 
Lulen 

R.,  .Sept.  22.  '06.. 
R..  Feb.  10.    06 

14 
1» 

190«    H. 

25.680 

97 
98 
00 

4x 

Ju  son.... 

N.,  Auk.   1.  '01 
R..  Apr.  20.  '06 

E.C..  Sept.  2,  'OS 

1  4  75 

■•^U,         -^: 

'            lf.O 

18 
21 

H. 

K.  a. 

" 

14J,900 

Con  Crete  Steel  Co. . 
Osborn 

.  13. 40101 
.....    1C2 

103 

2.1SJC4 

1.84105 

!K6 

19061  H. 
1897^    " 
1907  E.  R. 

77,000 
5,040 

1  J.900 
75,000 

12.600 

Burr 

Dean 

Lutcn 

N,  May   9,  '07 

R..  Dec.  10,  '98 

11 

20 

8"  1 

4'^ 
Frame 

36 

8 

18 
18 

21   1903    H. 
24   1896     •• 

CourtriRht. ... 
Brady 

N..  Mav  12.  '04 

R..  Nov.17,'00 
N.,  Apr.  6,  '05 

.     i  1  96107 
.       S.:01C8 

10 

1904  F.  B. 
1896i   H. 

Il09 

10 

fi"  1 

T 

36 

Mclan  Con.  Co  . .  . . 

110 

.   .1   .     E.  R. 

6   1902    ... 
12  1907  E._R. 

12  1905    H. 

Mercereau 

111 

112 

..  1  4.31 

17 

Luten 

.     '  ..      113 

14 

114 

9 

Luten. ...                                 ' 

1 

115 

N.,  Oct.  19.  '99 



116 

10 

5"'l 

12  i;k)2  H. 

... IJOO  

4  ,  . .  i   H. 

« 

IJ7 

Hewctt.          1 

118 

15 

Luten 

1 

1t» 

14 

i 

liO 

1.3 

8 

■•■:;:::••■::;:::. i 

1?1 

26    

1905  U.  R. 

12,000, 

E.C.,  Sept.  2,  'OS 

6.53 

122 

! 



1 

I 


^ 


r  I 


"I 

Ir 


h  .. 


If! 


t 


m 


m 


at 


it 
s 


^  X 

S  ^ 


X 

at 
X 


1m) 


It 


X 


I 


IffOS 


PART  III. 

Highway  Beam  Bridges. 
Comparison  of  Arch  and  Beam.  I'iio  advj 
<«r  arch  Itridjrcs  havo  already  boon  described  in 
Part  I  (.i*  this  l)ook,  and  original  formulae  have 
bc«'ii  jjiven  from  which  the  approximate  cost  of 
eonerete  bridfjes  may  be  determined.  One  of  tlie 
chief  merits  of  arch  liridges  i.s  that  Avhen  properly 
desijrncd,  Ihey  may  be  made  beautiful  in  outline. 

Some  of  the  advantages  of  beam  bridge.s  are  as 
follows:— (1)  It  is  possible  in  a  beam  bridge  to 
locate  the  grade  of  the  bridge  floor  much  lower  and 
nearer  to  the  high  water  level  or  other  clearance 
line  than  can  be  done  when  an  arch  is  used;  (2) 
foundations  for  beam  bridges  may  be  built  on  soil 
tliat  is  more  or  less  yielding,  which  cannot  be  done 
with  arch  l)ridges.  unless  liinges  are  used  at  the 
••enter  and  spring  The  lateral  thrust  of  arches  on 
soft  foundations  is  liable  to  cause  serious  injury  to 
the  structure,  while  the  corresponding  amount  of 
settlement  inider  the  abutments  of  beam  bridges 
produces  no  injurious  effect. 

A  fre(juent  objection  to  the  use  of  beam  bridges 
is  that  they  are  not  susceptible  to  artistic  treatment. 
It  will  be  seen,  however,  by  referring  to  '"igures  37, 
38  and  39,  that  beam  bridges  may  be  designed  that 
are  equally  piea;-"  ig  in  appearance  to  arch  bridges, 
and  for  many  locations  are  more  suitable. 

In  making  a  sc-lecti.r.n  between  an  arch  and  a 
beam  design,  the  chief  consideration  will  generally 

181 


ib' 


a. 

V. 


X     /J 


y. 


IIIGIUVAY    HI. AM       KlDGliS. 


183 


l)t'  tln'ir.  n'lativf 


1 


cost.     Tlic  ('(tst   of  (•(uicrpto  arcli 


l»ri<lir.'s    1ms   filrcjidy    hccii    jjivoii    l>y    tlic    fornuil} 
n-t'crn'd  t<>  }|Im»vc.  uvA   for  the  purpose  of  cniupHr- 
isuii.  ilic  costs  of  concrete  hciiiii  lirM 
fjin^riiij:  from  4  to  40  feet   in  lrii<' 


p's.  Ill  spans 
arc  ffiven  in 


t'n-  fiihics  (III  Figures  :!S  niiil  .W)  i'lie  estiniatetl 
••osls  of  these  Ix-ain  hridjres  ineludo  \\\c  filling,',  pave- 
ment and  two  lines  of  railinj;.  hut  (lo  not  include 
lamps  or  other  purely  ornamental  features.  On 
l''i<;ur.'  ;;s  is  <;iv.  ,  ,ds.i  a  tahh-  of  approximate  eosts 
for  concrete  ahiitments  of  various  heights,  which 
••slimates  also  include  railing  and  pav<uient  to- 
gether with  earth  excavation  an<l  hack  filling  in  th.« 
ahiitments.  These  estimates  will  enahle  the  de- 
signer to  eompare  the  relative  cost  of  nrch  an  1 
beam  liridges.  and  to  seleet  the  form  which  he  finds 
iiiosl  .  conomical. 


TABLE  IV 


SlMW 


l.i-nKth 


ABrTMKNT* 


Crvit 


HelKht 


Beam  Bridges.  Concrete  beam 
built  in  spans  up  to  70  feet  in  le 
not  generally  economical  for  len 
feet,  for  above  this  length  arch 
the  least. 


♦  -. 

4 

t  380 

nc 

3tll 

150 

410 

aw 

5111 

250 

« 

«5II 

810 

9 

770 

370 

10 

HNO 

4  to 

11 

io:«i 

510 

12 

lliX) 

('"«t 


bridges  have  been 
ngth,  but  they  are 
gths  exceeding  35 

bridges  will  cost 


3- 
M 


Ii-h'' 


i  •  1 M  • 


:| 


I      ■  1    i 


L 


184 


c 


& 

et 

en 

Z 

c 
u 

s 
< 


n   a. 

^    >- 
as 

e 

> 

< 

B 


H 

O 

u 


tllGHlVAY  BEAM   BRIDGES. 


185 


The  economical  lengths  and  forms  for  concrete 
beam  bridges  are  as  follows:  Simple  slabs  are  eco- 
noniieal  for  spans  up  to  12  feet.  Beam  bridges 
similar  to  Figures  37  and  39,  supported  on  parallel 
longitudinal  beams,  are  economical  for  spans  from 
12  to  25  feet  in  length,  while  above  2~)  feet  it  is 
economy  to  use  two  lines  of  heavy  side  beams  carry- 
ing light  cross  beams  supporting  the  floor  slab. 

To  determine  the  economic  span  length  to  use  in 
a  long  bridge  containing  several  intermediate  piers, 

TABLE  V 


Side  Beam 

Center  Benin 

Kntiniate 

Span 

Cone. 

Rods 
Ft.  In.Sq. 

Cone. 

Rods 
Ft.  lu.  S.J. 

Cone. 

Steel 

Cost 

Ft. 

Cu.  Yds. 

Lbs. 

8 

12x30 

2-    ?.i 

12x16 

3  -    'i' 

3.8 

656 

$  164 

10 

12x-.i0 

2-    \ 

12x18 

3-    '4 

4.9 

850 

207 

Vi 

12x20 

3-     'a 

12x20 

*-     ?4 

6.1 

1160 

256 

14 

12x20 

3-     % 

12x23 

4-     »4 

7.3 

1360 

304 

16 

12X21 

3-1 

12x27 

4-     ', 

8.9 

1780 

360 

18 

14x22 

3-1 

14x28 

4-     \ 

11.2 

2()(K) 

420 

20 

14x25 

3-l'„ 

14X112 

4-1 

13.3 

2550 

490 

22 

14x28 

3-1'a 

14x35 

4-1 

15.5 

2800 

645 

'ii 

14x31 

4-1 

14x39 

4-l'« 

16.2 

3350 

603 

26 

14x34 

4-1 

14x42 

4-l'„ 

20,7 

3620 

682 

28 

14x37 

5-1 

14x46 

6-1 

23.8 

4460 

775 

30 

16x38 

5-1 

16x46 

6-1 

28.2 

4770 

865 

32 

16x41 

6-1 

16X.W 

6  -  1'8 

32.0 

5800 

960 

34 

16x44 

6-1 

16x54 

6-l'8 

35.7 

6200 

1090 

36 

16x48 

7-1 

16x57 

8-1 

39.8 

7000 

1140 

38 

16x52 

7-1 

18x58 

8-1 

45.5 

7450 

1244 

40 

16x56 

7-l'« 

18x62 

8.1'8 

61.2 

9400 

1400 

the  nile  is  to  select  such  a  span  length  that  the  cost 
of  one  span  will  be  approximately  equal  to  the  cost 
of  a  pier. 

Methods  of  Design.  Single  span  concrete  bridges 
of  either  slab  or  beam  design  must  be  considered 
non-continuous,  but  for  a  series  of  spans  the  effect 
of  continuity  in  the  beams  may  be  considered.  To 
provide  for  this  continuity,  it  is  customary  to  pro- 


18C 


co.xch'jru:  bridges  .i\n  ciut.rts. 


11 , 


I  :i  I   ' 


I)(>rti()n  the  boains  for  only  80^^  of  the  maximum 
hciulins  moment.  Tlie  floor  slabs  must  be  pro- 
tected from  injury  by  a  sufficient  depth  of  earth 
i'illing,  M-hieh  is  shown  12  inehes  on  Fii,'ures  ;18  and 
■)!).  This  provides  depth  enouf,'h  for  beddinjr  ties 
of  street  railway  tracks.  A  suitable  pavement  or 
wearing  surface  may  be  laid  on  this  earth  fillin},' 
which  may  be  renewed  as  recpiired. 

It  is  permissible  and  good  practice  in  designing 
small  concrete  beams  which  are  united  by  slabs,  to 
consider  the  effect  of  a  i)ortion  of  the  floor  slal) 
and  to  projjortion  the  beams  as  T  beams.  Large 
longitudinal  beams  carrying  floor  loads  directly  to 
the  piers,  should  be  proportioncnl  as  simple  beams 
without  considering  the  effect  of  the  adjintiingslab. 
They  will  then  have  additional  strength  due  to  the 
l)resence  of  such  slab. 

The  bridges  shown  in  Figures  .18  and  3f)  are  de- 
signed for  total  loads  of  from  400  to  500  pounds 
per  S(|uare  foot  of  floor  surface.  It  is  customary 
to  provide  for  impact  either  by  adding  a  percentag'^ 
to  the  live  load  or  by  using  a  factor  of  2  for  dead 
load  stresses,  and  a  corresponding  factor  of  4  for 
live  load  stresses. 

It  has  been  proven  by  numerous  experiments  that 
the  adhesion  of  concrete  to  metal  is  sufficiently 
great  so  no  additional  bond  is  required,  but  as 
voids  in  the  concrete  are  liable  to  occur  and  it  is 
difficult  to  always  secure  the  highest  grade  of  work- 
manship, it  is  desirable  to  use  rough  bars  with 
mechanical  bond.     As  provision  mast  also  be  made 


f'^3r"-m 


niGinVAV    BEAM    BRIDGES. 


187 


fur  shear  by  the  iiso  of  inclinoil  or  bent  rods  and 
stirrup  irons,  it  is  desirable  in  all  large  beams,  to 
nsc  reinforeing  bars  whidi  have  the  inclined  stir- 
rups or  shear  members  rigidly  connected  to  the 
main  tension  metal. 

Til  all  bridges  where  appearance  is  any  consider- 
ation, the  railing  should  be  designed  Avitli  care  so 
the  design  may  properly  harmonize  with  the  rest 
of  the  structure.  CJenerally  speaking,  the  balus- 
trade that  presents  the  best  appearance  on  a  con- 
ciM'te  bridge  is  one  composed  of  either  natural  or 
artificial  stone,  but  it  is  also  evident  (Figure  39) 
that  an  cfpially  artistic  eflTect  may  be  secured  with 
ail  ornamental  metal  railing  and  stone  or  concrete 
])osts  and  pedestals.  Open  balustrades  are  usually 
l)i-('ferable  to  solid  ones,  not  only  because  they  are 
susceptible  to  more  artistic  treatment,  but  also  be- 
cause their  light  and  open  design  emphasize  by  con- 
trast the  solidity  and  strength  of  the  supporting 
structure  ])eneath  them.  Solid  balustrades  are  per- 
missible chiefly  for  through  bridges,  where  the  con- 
crete side  girders  standing  above  the  roadway  form 
a  sufficient  protection.  The  exposed  girder  surface 
may  then  be  paneled  or  otherwise  ornamented. 


r»it'!!^^« 


I  n[i| 
f   l>  i 


!i 

[J 

1 


■  i  :  ! 


lan 


<^^m^^ 


iM>it&.- 


X 

> 


5 

'  s 

•■r. 

u 

u 

as 
'■J 
z 


PART  IV 

Concrete  Culverts  and  Trestles. 

Since  the  iiitroduetioii  of  reinforced  eoi  -rete  as  a 
building  material,  nii,.iy  railroad  companies  are  re- 
buildinj?  their  permanent  bridges  and  culverts  in 
concrete,  either  plain  or  reinforced.  The  use  of  re- 
inforced concrete  for  culvert  construction  has  be- 
come almost  general  with  the  railioad  companies, 
while  the  building  of  trestles  in  this  material  i:s  grad- 
ually raming  into  favor.  :Many  old  wooden  struc- 
tures, both  of  the  open  and  tl:c  gravel  deck  types, 
are  being  replaced  by  better  ones  of  concrete  ma- 
sonry. Amor.^'  the  railroad  companies  that  are 
using  reinforced  concrete  extensively  for  the  con- 
struction of  trestles  may  be  mentioned  the  Illinois 
Central,  the  Cleveland.  Cincinnati.  Chicago  &  St. 
Louis  (Big  Four),  and  other  branches  of  the  New 
York  Central  Railroac'  system.  A  notable  concrete 
trestle  or  viaduct  that  has  attracted  much  attention 
is  the  one  recently  built  at  Richmond.  Virginia,  for 
the  Richmond  &  Chesapeake  Bay  T?ailroad  Com- 
pany. This  viaduct  is  2,800  feet  ir  length,  and 
varies  in  height  from  18  feet  at  the  ends  to  70  feet 
near  the  middle,  and  is  shown  in  Figure  40.  At  At- 
lanta, Georgia,  there  is  a  reinforced  concrete  viaduct 
carrying  Nelson  street  over  the  tracks  of  the  South- 
ern Railroad.  It  contains  10  spans  of  various 
lengths  from  20  to  l:^  fo,>t.  has  a  total  length  of  480 
feet,  and  is  shown  in  Figure  41.  The  main  line  of 
the  Big  Four  Railroad  is  carried  for  a  distance  of 

188 


'■  \ 


II!    ^ 


i 


If 


100 


COXCRLIL   BRWGl.S  AXD   CLLl'LKTS. 


1.200  foot  across  the  Lawrenceville  Bottoms  on  a 
rciiiforeo'l  ooneroto  trestle  20  feet  in  height.  This 
entire  rcfifion  is  pcriodii-ally  Hooded  Avith  baekwatci- 
i'fniii  the  Ohio  and  Miami  rivers,  making  it  neees- 


FlK.  41. 
.NKLSO.N  STKKKT  VIAUUCT,  ATL.ANTA,  GKORGU. 

siiry  to  bnild.  not  only  this  road,  but  all  others  in 
tile  vii-iiiily  at  an  cb'vation  of  ;}0  feet  above  h»w- 
Avater  level  of  the  Oliio  River. 

On  tli(  following  pages  are  designs  and  estimates 
for  about  1.000  railroad  culverts  and  trestles,  and 


CONCKETli    CLLlliUIS     IXP    TKES Fl.LS. 


191 


the  cstunatetl  costs  are  given  on  charts  shown  in 
Figures  4G,  47  and  66. 

Tt  will  be  seen  tha  the  trestle  designs  are  equally 
suitable  for  culverts,  and  may  he  adapted  for  that 
purpose  l)y  iiuTcasing  their  width  to  correspond 
with  the  depth  of  structure  hclow  the  base  of  rail, 
or  to  confonn  to  the  depth  of  the  enibaidanent. 
When  used  as  culverts,  abutnu'ut  wing  walls  must 
l)e  added  and  the  nature  of  the  f(>undation  soil  » my 
be  such  as  to  reipiire  culvert  pavement.  These 
nu)difications  in  the  trestle  estimates  may  easily  be 
made  either  for  one  or  more  openings,  and  adapted 
for  either    ingle  or  double  box  culverts. 

The  culvert  designs  are  shown  with  a  minimum 
depth  of  filling  of  not  less  than  3  feet  above  the  con- 
crete top.  This  depth  is  desirable  not  only  for  the 
purpose  of  distributing  the  live  load  from  the  engine 
and  train  wheels,  but  also  for  the  pnipose  of  form- 
ing a  cushion  to  absorb  and  distribute  the  shock 
and  impact  from  rapidly  moving  trains.  Trestle  de- 
signs G  and  II,  Figures  64-65,  are  shown  with  a 
:?-foot  depth  of  filling.  It  freiiuently  occurs,  how- 
ever, that  thin  floors  are  necessary  and  only  suf- 
ficient depth  can  be  secured  for  the  usual  1.')  inches 
of  ballast.  This  arrangement  has  been  shown  in 
trestle  designs  A  to  F  inclusive.     (Fig\u-es  r)S  to  6:}.) 

Required  Size  of  Culvert  Opening. 

The  nu)st  important  consideration  effecting  the 
final  cost  of  a  culvert  is  the  selection  of  its  form 
and  size.     It   freciuently  occurs  that  structures  of 


iL-».MHliJUL'. 


.'BW'MJillWtii'illi* 


I' 

i  1 


"ini 


192       CO-y CRETE   BRIDGES  .IXD  CULVERTS. 

too  large  a  size  and  oxeossive  cost  are  specified, 
when  smaller  ones  would  be  ample  to  carry  off  the 
greatest  rainfall. 

The  selection  of  the  proper  size  of  cnlvert  is  of 
much  greater  importance  than  any  consideration  of 
design.  If  a  culvert  costing  .tlO,0()0  be  specified, 
where  a  snuiUer  one  costing  only  iji.l.OOO  would  be 
sufficient,  the  loss  by  such  an  error  would  evidently 
be  $r),000.  On  the  other  hand,  if  the  size  of  struc- 
ture as  specified  be  used,  the  engineer  may  by  care- 
ful estimating,  select  a  form  with  the  required  wa- 
terway, and  with  a  cost  of  only  .^8,000.  The  saving 
in  this  case  is  only  .'i;2.000.  whereas,  if  greater  care 
had  been  given  to  the  selection  of  the  proper  size, 
there  might  have  been  a  saving,  not  only  of  this 
$2,000,  but  of  ^:).{)00  additional.  It  will  be  seen, 
therefore,  that  the  one  consideration  outweighing  all 
others  in  efTecting  the  final  cost  is  the  selection  of 
a  structure  with  the  necessary  waterway. 

In  the  State  of  Wyoming  there  are  four  bridges 
within  a  short  listance  of  each  other,  carrying  a 
road  over  the  same  stream.  The  last  of  these 
bridges  to  be  built  has  two  spans  G.')  feet  in  length, 
or  V.\()  feet  extreme.  The  second  bridge  has  two  40- 
foot  spans,  and  is  SO  feet  in  length.  The  third  has 
a  single  GO-foot  span,  Mhile  the  fourth  is  an  old  30- 
foot  wooden  truss,  which  has  for  fifty  years  proved 
itself  sufficient  to  meet  even  flood  conditions.  There 
are,  therefore,  in  clo.se  proximity  to  each  other  four 
bridges  over  the  same  stream,  the  longest  of  which 
is  four  times  greater  than  the  shortest,  and  the  long- 


CONCRETE    CULVERTS   AND    TRESTLES.     193 

est  one  was  the  last  one  built.  After  selecting  a 
length  of  structure  four  times  greater  than  required, 
it  is  possible  that  the  engineer  may  have  spent  con- 
siderable time  and  thought  in  his  endeavor  to  build 
tliis  bridge  at  the  least  possible  cost,  and  may  have 
succeeded  in  saving  a  few  hundred  dollars  on  his 
original  estimate.  • 

A  bridge  130  feet  in  length  would  cost  approxi- 
mately .$7,000,  while  a  30-f()ot  bridge  would  not  ex- 
ceed $1,500.  This  saving  is,  therefore,  only  a  frac- 
tion of  the  saving  that  might  have  been  effected, 
had  a  30-foot  bridge  been  used,  which  length  had 
proved  sufficient  for  half  a  century. 

The  most  reliable  data  on  which  to  base  the  size 
of  a  prospective  structure  is  the  high-water  level  of 
previous  years.  It  is  Trequcntly  possible  to  obtain 
such  data  from  local  records,  or  to  determine  the 
size  from  that  of  other  bridges  passing  the  same 
tlow  of  water  in  the  near  vicinity.  In  the  case  re- 
ferred to  above,  if  the  engineer,  before  building  the 
130-foot  bridge,  had  made  sufficient  inquiry,  he 
could  easily  have  learned  that  a  30-foot  span  had 
carried  the  entire  stream  discharge  for  fifty  years, 
and  was  therefore  large  enough  for  the  raintVill  of 
the  future. 

It  is  not  economy  to  provide  openings  of  sufficient 
size  to  carry  the  rainfall  of  freshets  or  cloudbursts 
that  may  not  occur  oftener  than  once  in  a  century. 
For  such  unusual  occurrences  it  is  better  to  make 
occasional  repairs  than  to  invest  additional  money 
in  larger  structures  than  may  ever  be   required, 


r 


m 


194        LOXCRETE   BRIDGES  JXD   CiLrEKTS. 

when  Hiicli  iiioiicy  niiglit    bo    drawing    iiitorost    to 
cover  the  cost  ol"  an  occasional  repair. 

Where  reliable  data  in  reference  to  the  niaxinniin 
rainfall  cannot  be  obtained,  it  is  customary  for  the 
railroads  to  build  temporary  wooden  trestles  at  the 
proposed  bridge  or  culvert  site,  and  to  make  thes.; 
trestles  unnecessarily  long,  so  there  will  be  no  doubt 
whatever  of  the  openings  being  large  enough.  These 
temporary  bridges  will  last  from  six  to  ten  years, 
and  during  this  period  careful  observations  of  the 
water  flow  may  be  made,  and  other  data  secured 
from  which  to  determine  the  necessary  culvert  area. 
As  the  cost  of  these  temporary  trestles  will  not  ex- 
ceed !f<10  per  lineal  foot  their  entire  cost  may  easily 
be  saved  by  selecting  the  minimum  reciuired  size  for 
the  permanent  structure. 

"Where  no  reliable  data  in  reference  to  the  volume 
of  water  is  obtaiiud)le,  the  culvert  area  may  be  coir.- 
puted  approximately  by  a  empirical  rule  known  as 
>Ioyer's  Formula,  which  is  as  follows: — The  Re- 
quired Culvert  Area— ^  Drainage  area  in  acres  X  F, 

where  F  is  a  eoeifieient  varying  from  unity  for  tiat 
country,  to  4  for  rolling  or  mountainous  country, 
from  which  rainfall  is  discharged  at  a  greater  ve- 
locity. The  proper  value  for  this  coefficient  for  any 
particular  loention  must  be  selected  entirely  by  the 
judgment  of  the  engineer. 

Reinforced  Concrete  Box  Culverts. 

The  following  series  of  designs  for  single  and 
double  box,  reinforced  concrete  railroad  culverts,  in- 


1 


COXCRBTE   CUWERTS   ASD    TRESTLES.     195 

.'ludos  between  800  atnl  000  separate  estimates,  and 
is  therefore.'  very  comprehensive  and  complete.  Tlu« 
charts  of  eomparative  eosts,  Fif?nres  46  and  47.  show 
these  to  be  more  economieal  than  any  other  form  <>f 
culvert,  excepting  perhaps  reinforced  concrete  oval 
culverts  of  the  form  shown  in  Fifrure  57.  While  arch 
culverts  of  this  latter  form  may  contain  less  ma- 
terial than  box  culverts  of  equal  area,  they  are  more 
(lilTicult  to  build  because  of  their  curvature,  even 
though  collapsible  centers  be  used.  Several  large 
railroad  systems  in  America  are  now  usiii;,'  arch  cul- 
verts of  this  general  form,  in  place  of  the  old  seg- 
m"Mtal  or  semicircular  types,  which  contain  more 
masonry  in  the  abutments  than  in  the  arch  wing. 

Loads.  There  is  much  uncertainty  in  refen  (<"» 
to  the  amount  of  load  carried  by  the  cover  of  a  rail- 
road culvert.  The  amount  of  this  load  depends  to 
a  great  extent  on  the  depth  of  the  culvert  top  l)clow 
the  base  of  rail.  The  greatest  load  occurs  when  the 
depth  of  filling  above  it  is  a  nMnimum.  for  then  the 
culvert  top  is  siibjected  to  the  entire  load  from  the 
locomotive  wheels  and  their  impact.  On  the  con- 
trary, when  the  culvert  is  buried  beneath  a  deep 
embankment,  the  live  load  and  impact  is  so  distrib- 
uted and  dispersed  that  only  a  part  of  this  loid  goes 
direclly  to  the  culv  rt.  Various  writers  have  en- 
deavored to  show  that  these  loads  are  distributed 
crosswise  of  the  embankment,  and  slope  outward 
from  the  railroad  ties  at  the  rate  of  one  foot  hori- 
zontal for  every  two  feet  vertical.  The  pressure  on 
the  base  of  these  triangles  varies  from  zero  at  the 


\'  i 


196       COSCRLTE  BRIDGES  ASD  CULVERTS. 

outer  point  to  a  maxiinum  uiulor  the  ond  of  tie.  This 
nssnniption  is  otily  an  approximation,  though  a  rea- 
sonable one.  T'nfortunatcly,  however,  the  author  of 
this  liypothesis  assumes  that  the  earth  pressures 
slope  outward  at  each  side,  hut  makes  lu)  provision 
for  similar  distribution  lengthwise  of  the  embank- 
ment. It  is  (juite  evident  that  whatever  distribution 
of  loads  does  oeeur,  nuist  oeeur  e(|ually  in  all  direc- 
tions, and  the  assumption  referred  to  above  is  there- 
fore incorrect. 

"Where  a  culvert  has  a  small  depth  of  filling  above 
it,  the  entire  weight  of  such  filling  is  then  suj)- 
ported  by  the  culvert,  but  if  located  at  the  bottotix 
of  a  high  embankment,  the  culvert  then  carries  only 
a  portion  of  the  live  load  above  it,  supporting  also 
a  i»ortion  only  of  the  earth  embankment.  The 
amount  of  this  portion  depends  upon  the  nature  of 
the  embankment  material.  If  this  material  is  ce- 
mented wi'll  together,  it  will  then  tend  to  support 
itself  by  acting  either  as  an  arch  or  beam,  and  there- 
by relieving  the  culvert  of  much  superimposed  load. 
The  uKist  reasonable  assumption  is  to  consider  that 
the  culvert  carries  the  weight  of  a  triangular  sec- 
tion of  the  embankment,  the  sides  of  which  slope 
outward  from  the  vertical  in  the  ratio  of  one  foot 
horizontal  to  two  feet  vertical.  If  the  embankment 
material  is  composed  of  clean  sand,  a  larger  propor- 
tion of  the  imposed  nuitcrial  will  then  be  borne  by 
the  structure.  In  view  of  the  uncertainty  of  various 
conditions  efl'ecting  the  amount  of  load  on  culvert 
tops,  it  has  been  deternnned  that  these  loads  can 


CONCRETli    CVI.ILKIS    J.V/»    TRESTLES.      197 

never  cxcood  the  values  oeeurririff  uiidor  a  miniiniim 
depth  of  earth  filling. 

An  assumed  live  load  on  oaeli  traek  eriuivalent 
♦o  Cooper's  eni^ine  load  K.  ."»().  spread  <»ut  l)y  the  ties, 
calls  and  l)allast,  produces  a  distributed  load  on  the 
eulvert  top  of  1,100  pounds  per  scpiare  foot.  To 
this  has  been  ad«led  impact,  amounting  to  50% 
of  the  live  load,  or  '^'yO  pounds  per  sfjuare  foot. 
Adding  to  these  the  ^veight  of  ties,  rails,  ballast, 
earth  filling  and  eonerete  in  the  culvert  top,  pro- 
duces a  total  load  of  from  2,100  pounds  per  square 
foot  for  small  culverts  with  thin  slabs,  to  2.400 
pcmnds  per  scpiare  foot  for  larger  spans  with  a 
greater  thickness  of  concrete.  The  following  box 
culvert  tops  are  therefore  proportioned  for  total 
loads  of  from  2.100  to  2,400  pounds  per  square  foot. 

From  the  theory  of  horizontal  earth  pressure,  it 
is  known  that  the  thrust  per  s(iuare  foot  on  an  em- 
bedded vertical  surface  is  v  pial  to  one-third  of  the 
corresponding  horizontal  pressure  on  a  unit  •'*  area 
at  the  same  level.  This  condition  exists  when  the 
einbankmcnt  is  comi)osed  of  clean,  dry  sand  with  an 
angle  of  repose  of  about  HO  degrees.  The  proper 
amount  of  pressure  to  assutiK  on  the  culvert  side  is 
therefore  from  700  to  800  pounds  per  scpiare  foot, 
or  one-third  of  the  corresponding  roof  loads.  As 
the  sides  are,  however,  subjected  to  vertical  loading 
and  impact  from  moving  trains,  th"  .assumed  side 
pressure  has  been  taken  at  one-half  of  the  vertical, 
or  from  1,050  to  1,200  pounds  pci   upiare  foot. 

On  account  of  the  liberal  provision  for  impact, 


mm. 


'■^"■^BB? 


f( 


198 


COXCRETl-    BKIDGIiS  AXD   CTU'ERTS. 


amounting  to  50%  of  the  live  load,  high 
^vorking  values  have  been  used  for  concrete  and 
metal  reinforcement.  A  reasonably  rich  concrete 
mixture,  such  as  1-:}-"),  lias  an  ultimate  crushing 
value  of  2,800  pounds  per  s(|uare  inch.  One-f<mrth 
this  amount,  or  TOO  ponnds  per  stpiare  inch,  is  there- 
fore assumed  as  a  working  unit  for  concrete,  ami 
12.000  pounds  per  square  inch  as  a  working  unit 
for  reinforcing  steel. 

Economic  Length  for  Slabs  and  Beams.  There  is 
evidently  a  limit  where  economy  ce;ises  in  the  use 
of  flat  slalxs  for  supporting  loads  in  bending,  and 
above  that  limit  the  economical  construction  is  a 
eombiiuition  of  Ix-ams  and  shibs.  For  the  purpose 
of  determining  tliese  economic  lengths,  a  slab  tal)le 
(Tai)le  No.  VI  i  lias  been  prepared,  giving  the  amount 
of  concrete  and  steel  and  the  estimated  cost  per 
s(iuarc  foot  for  spans  varying  in  length  from  -4  lo 
24  feet,  and  total  imposed  loads  of  from  2,100  to 
2.400  i)ounds  i)er  scjuare  foot. 

TABLE  VI 

REINFORCED  CONCRETE  SLABS— SIMPLE  SPANS 
TOTAL  LOADS  2100  TO  2400  LBS.  PER  SQUARE  FOOT. 


Kff.Ttivo 

T<.l,il 

pan. 

Depth. 
6 

Dcptli. 

1    .  .*> 

s,,.  n 

4 

;'4  ill.  7  1  J 

6 

9 

11)  .-> 

'    s                    1 

8 

12 

1  :t  :. 

\      "       .-.1.^ 

10 

1.5 

17  0 

"       ."ll.l 

12 

18 

JO  0 

"    4'.". 

14 

21 

J.-j  (1 

•    4   " 

16 

24 

Jl)  (1 

<i  ••  .-.1.; 

IS 

28 

:«)  :> 

U   "    4  '.", 

20 

.^t 

.>•»..» 

U     '    4    ■ 

■>•! 

:n 

;t7(i 

+  "  ;{'V 

jj 

.{7 

M)  t) 

4  ••  ;{'. 

in  apart. 


Cost 

prr 

sciuaro  ft. 

(Viits. 

:<() 

« 

4.{ 

f) 

:.6 

0 

71 

I) 

S."i 

■" 

97 

t 

110 

•> 

i:n 

.1 

140 

.) 

159 

0 

170 

0 

1 


CONCRETE    Cr EVERTS    AXD    TRESTEES.      199 

A  corresponding  set  of  ten  tables  was  made  giv- 
iiij,'  the  anionnt  of  material  and  the  estimated  costs 
pi'r  scfuare  foot  for  a  combination  of  beam  and  slab 
coiistrnction,  Avith  spans  varying  from  6  to  30  feet 
ill  length,  and  beams  spaced  from  6  to  18  feet  apart, 
on  centers.  The  cost  results  from  these  ten  tables 
are  given  on  the  chart,  Figure  42.  The  thickness 
oF  slabs  and  beams  are  proportioned  so  the  stress 
iit  the  outer  edge  will  not  exceed  700  pounds  per 
sijuare  inch  from  dead,  live  and  impact  loads.  The 
thicknesses  Avere  determined  from  the  "writer's  orig- 
ii:al  formula 

M 

K 


d^ 


V.  licrc  ]\I.  is  the  bending  moment  in  inch  pounds, 

d    the  distance  from  slab  top  to  center  of  ten- 
sion bar.  and 
K  a  variable  factt>r. 

It  is  advisabk'  to  neglect  the  effect  of  continuity 
ill  proi)ortioning  sla])s,  even  though  a  considerable 
.•I mount  doul)tless  exists,  whicli  wovdd  reduce  the 
shib  thickness  by  about  2(V/( .  Slab  thicknesses  are, 
llii'refore,  given,  as  re<[uii'ed  for  non-continuous 
licains.  From  the  comparative  cost  chart,  Figure 
42.  the  following  conclusions  are  obtained.  For 
loads  of  from  2,100  to  2.400  i)ounds  per  sciuare 
foot  :— 

Simple  slabs  are  ccoiioiuical  for  clear  spans  up  to 
7  feet  in  length. 

Sljibs  with  beams  (5  fcot  apart  wn^  ccononiic.Ml  for 
spans  from  7  to  14  feet  in  length. 


n 


i  I 
i 


III! 


i  :| 


200        CONCRETE   BRfDGES  AND   CULVERTS. 


P 


?: 


:i 


Comparative  Cost  per  Sq.  Ft. 

Combination  of  Slabs  and  Beams  for 

Various  Beam  Spacing  also  Cost 

of  Simple  Slabs. 

Total  loads  210O  to  2100  lbs.  sq.  ft. 


S  Pans. 

i'lg.  42. 


26- 


So 


3o 


CONCRETE    CrU'ERTS   AXD    TRESTLES.     201 

Slabs  with  beams  7  feet  apart  are  economical  for 
spans  from  14  to  20  feet  in  length. 

Slabs  with  beams  8  feet  apart  are  economical  for 
spans  from  20  to  30  feet  in  length. 

The  comparative  cost  chart,  Fignre  42,  was  ob- 
tained from  130  separate  estimates,  and  the  conclu- 
sion from  it  is  that  slabs  for  the  above  loads  are  not 
economical  for  greater  lengths  than  8  feet  or  greater 
thicknesses  than  12  inches. 

Figures  43,  44  and  45  are  typical  drawings  for 
single  and  double  box  railroad  culverts  for  both 
slab,  and  a  combination  of  beam  and  slab  construc- 
tion, and  Tables  VII,  VIII,  IX  and  X  give  the  cor- 
responding sizes,  (luantities  and  costs  for  culverts 
varying  in  area  from  4  to  480  square  feet.  These 
tables  give  separately  the  rjuantities  and  cost  for 
the  two  portals  and  for  the  culvert  barrel  per  foot 
of  length,  and  also  the  lengths  and  total  costs  of 
culverts  for  six  different  heights  of  embankment, 
varying  from  10  to  50  feet. 

The  single  and  double  slab  culvert  tables  contain 
34  different  sizes  each,  varying  from  2  feet  by  2 
feet  to  12  feet  by  12  feet  for  each  opening,  while  the 
combined  beam  and  slab  culverts  contain  30  corre- 
sponding sizes  each,  varying  from  8  to  20  feet  in 
width,  and  from  4  to  12  feet  in  height.  The  esti- 
mated costs  of  these  culverts  for  banks  20,  30,  40 
and  50  feet  in  height  are  shown  in  Figure  46.  These 
<Mivves  represent  the  cost  of  the  economic  forms, 
which  generally  have  openings  of  a  greater  height 
than  width,  such  as  4  feet  wide  by  6  feet  high,  either 


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TABLE  VII 

TO  ACCOMPANY  FIGURE  43 


'T..pan,l  H„tt.,„,'        Si,l,.s.  Onantitie»,M'rlin.f, 


S:    i 


2  r.irlals. 


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9 
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20 

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2510  4   4017 


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28  "10100  "  •' 

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3012  4  4820  I 
31  i  "  6,  72  '■  ■ 
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33  "10120  "  " 
34'  "12144  "  " 


1  —51. 


41. 


8 
9 
10 
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9 
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12 
12  ■ 
12  • 
14  • 
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15 
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18 
IS 
IS 
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20 
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10 
—  18 
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12 
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18 
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8 
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s 
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12 
10 
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12 
12 
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15 
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.28 

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.69 
.  55 
.64 
.74 


22: 

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35 

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62 
58 
55 
65 
75 
92 
66 
75 
86 


2.43 

2  91 

3  69 
4.50 

5 .  39 

6 ,  55 
5.25 


1.7s 
3.40 

3 .  55 
4.00; 

4 .  5o: 

6.00 
3.85 


5.60  4.30 


6.66 
7.75 
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7.06 
8.10 


9  42 


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8 .  50 


14 

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250  58 
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250  54 
300  66 


500 
500 
600  65 
800'  84 


89 
72 


79101  10. .i7  10. 40  1000107 
0U32j  13.6013.00  1600136 
831131  11.2210.00)  900116 
12. 97 12.40' 1200147 
16  3013. 70  1S00173 
20. 60  15. '0  2200208 
15.0012.00l  900132 
18. 00 22. 00!  1800248 


.96134 
.20168 
.4    216, 
.18  139 
.33185 
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.  76  265; 
.712411 
.84  2661 
.07282i 
.503241 
,88381' 
33327' 
56362; 
7s;j78 
00412 
40466 


20.4030.00' 2200328 
24.7043.00  3200472 
23.3018.00  1400200 
25.4028.00  2200312 
27.9037.00  3200424 
32.9046.00  4000528 
38.3057.00  5000656 
31.8023.00  1800256 
34  9037.00:  2.S(K) 378 
37.3052.00:4000576 
40.4068.00  5000744 
45.8082.00  6500916 


CONCRETE    CULVERTS   AND    TRErTI.ES.     205 


TABLE  VII— Continued 

REINFORCED  CONCRETE,  SINGLE  BOX,  RAILROAD 

CULVERTS— SLAB  CONSTRUCTION 

TO  ACCOMPANY  FIGURE  43 


10  ft.  Hank,  j  15  ft.  Bank.  \  20  ft.  Bank.  |  30  ft.  Bank.  \  40  ft.  Bank.  1 .50  ft.  Bank, 


2S  348 

2.')  365 

31  366 

2.^)  470 


30  .')82 


30  900 


29  1166 


39 

106 

36 

122 

39 

172 

35 

189 

32 

216 

29 

248 

3S 

230 

35 

230 

32 

26' 

29 

291 

2() 

330 

34 
'11 

312 

11  K 

54   145 
51,  175 
54  228 
50i  257 
47  296 
44'  346 
52'  318 
50  314 
47,  366 
44'  407 
41  467 
49  417 
46,  427 
43:  489 
40  532 
34;  598 
46  631 
40  662 
34  725 
28'  783 
45  807 
40  968 
34  1020 
28  1157 
45  1250 
39  1297 
33  1339 
27  1413 

44  i656 

38  1698 

32  1766 

26  1794 


1 

2 
3 
4 
5 
6 
7 
8 
9 
10 


59  2126 

53,  22 IS 
47  2326 
41  2394 
351  2516 


79i  1206 
91  1136 
85]  1247 
1453 
1708 
1482 
1778 
1938 
2262 
2300 
2442 
2594 
2888 
3176 
3076 
3278 
3436 
7i:  3804 
65;  3886 


400 
479 
611 
727 
859 
1033 
861 
1004 
1064 
1216 
143911 
1162|12 
129513 
1484  14 
1607  15 
201616 
1816,17 
2017118 
2433|19 
2928  20 
2382'2I 
2848,22 
3148:23 
3732  24 
3700  25 
3962,26 
424427 
484928 
5456  29 
4978130 
5348  31 
6676 '32 
6024  j33 
6636  34 


20f.      coxchT/in  BRinclis  .wn  cn.i'nRTS. 
TABLE  VIII 

REINFORCED  CONCRETE,  DOUBLE  BOX,  RAILROAD 

CULVERTS  -SLAB  CONSTRUCTION 

TO  ACCOMPANY  FIGURE  44 


r  :? 


1 

1     .J 

Top  aTiil  Bnttom 

t     J, 

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19  8   4,  64 

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2. 35:306 30. 901 4. d  900148 
2  6533833 . 7020 . 02000246 

2J   "    6:  96 

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21    ":  8128 

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2  95384  38 . 9027 . 02700304 

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26   "  10200 

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t .  70577,60 .  5047 .  04000536 

27   "12240 

(t 

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> .  1066066 .  8062 . 0  5000696 

2812  4|  96 

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29   "    6144 

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12    5 .  OS  GS5  67 .  60  35 . 0  2S00  392 

30  ")  8192' 

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S  " 

12    5.50 

70871.7045.04000520 

31   "10240 

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10   6.02 

759 78. 00 62. 050C J 696 

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1 

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8    6 .  55  838  85 .  00  75 . 0  6500  860 

, .  I  ^ 


COXCRIiTR    CVIA'RRTS   ASD    TRUST  I. ES.      207 

TABLE  VIII— Continued 

REINFORCED  CONCRETE,  DOUBLE  BOX,  RAILROAD 

CULVERTS— SLAB  COKsIRUCTION 

TO  ACCOMPANY  FIGURE  44 


10  II.H  k  1.5  ft.  Hank,  a)  ft.  Hank. :«»  fl.  Hank.  40  ft.  Hank.  .V)  ft.  Hank. 


B 

1 

200 

I 

5 

1 

s 

J 

"' 

^ 

5 

J 

\ 

54 

269 

66 

335 

99 

w 

- 

610 

l.-)9 

7.50 

m 

475 

I.i9 

1 

m 

201 

51 

272 

66 

341 

96 

482 

126 

623 

156 

763 

2 

Wh 

3  IT) 

50 

434 

65 

551 

95 

789 

125 

1029 

155 

1269 

3 

32 

347 

47 

486 

62 

625 

92 

905 

122 

1180 

152 

1470 

4 

29 

3cSl 

44 

542 

59 

706 

89 

1031 

119 

1356 

149 

1686 

5 

;i') 

414 

50 

569 

65 

729 

95 

1064 

125 

1384 

155 

1674 

(> 

32 

447 

47 

627 

62 

807 

92 

1172 

122, 

1522 

152 

1882 

7 

29 

471 

44 

676 

59 

881 

89 

1286 

119 

1696 

149 

2106 

8 

2« 

505 

41 

740 

56 

970 

86 

1440 

116 

1900 

146 

2370 

9 

:}4 

535 

49 

729 

64 

939 

94 

1337 

124 

1747 

154 

2147 

10 

:n 

555 

46 

780 

61 

1009 

91 

1459 

121 

1909 

151 

235!t 

11 

'_'S 

579 

44 

849 

58 

1079 

88 

1589 

118 

2089 

148 

2579 

12 

2:) 

(i22 

40 

906 

55| 

1196 

85 

1766 

115 

2316 

145 

2906 

13 

34 
h6 

984 
1094 

49 
61 

1344 
1414 

79 
91 

2044 
2044 

109 
121 

2754 
2684 

139 
151 

3465 
3324 

14 

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779 

15 

25 

802 

40 

1172 

55 

1532 

85 

2262 

115 

2992 

145 

3712 

16 

34 

1244 

49 

1684 

79 

2544 

109 

3414 

1.39 

4264 

17 

28 

1326 

43 

1856 

73 

2916 

103 

4086 

133 

5036 

18 

lioiOTU 

45 

1528 

60 

1998 

90 

2918 

120 

3848 

150 

4768 

19 

40 

1586 

55 

2096 

85 

3106 

115 

4116 

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5096 

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79 

3364 

109 

4.544 

139 

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3724 

103 

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133 

6424 

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45 

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2896 

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4276 

120 

5596 

150 

6976 

23 

39 

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54 

2968 

84 

4458 

114 

5i»38 

144 

740S 

24 

33 

2184 

48 

2984 

78 

4584 

108 

6174 

138 

7774 

25 

27 

2166 

42 

3066 

72 

4886 

102 

6786 

132 

8536 

26 

36 

3096 

66 

5096 

96 

7098 

126 

9096 

27 

2920.-12 

44 

2982 

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3932 

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119 

7882 

149 

9532 

28 

38 

2950 

53 

3960 

83 

5992 

113 

7990 

143 

10040 

29 

Z2 
26 

2800 
2716 

47 

3920 
3896 

77 
71 

6020 
6216 

107 
101 

8170 
8596 

137 
131 

10320 
10896 

30 

31 

35 

3830 

65 

6370 

96 

8960 

125 

11460 

32 

/y 


I  i 


t 


I 


208        COXCRI-.TI'.   liRIDGHS  ,1X1)   CULVllRTS. 

TABLE   IX 

REINFORCED  CONCRETE,  SINGLE  BOX,  RAILROAD 

CULVERTS— BEAM  AND  SLAB  CONSTRUCTION 

TO  ACCOMPANY  FIGURE  45 


\€ 


-      1^ 

■.~   IE: 


lop  and  Ituttom 

I  Si|uarc 
KuIh. 


S<iuare 
I    Kwla. 


I>r  Lineal  ft. 

■3 


2  Portak 


"■-a" 


I-    *.      I 


J3 


J  III 


1 

2 

3 

4 

5 

6 

7 

8 

9 

10 

11 

12 

13 

14 

15 

16 

17i 

18 

19 

20 

21 

22 

23 

24 

25i 

26! 

27 

28 

29 

30 


8  4 
"   6 

"   8 


3212314 

48   •'    "•• 
64   "    "•' 
"  10  80   "    'V 
10  4  4014364 

60   "    'V 
80  "    "," 


V 


1', 


•'    6 

"10100 
"12120 
12  4  4816404 

"6  72  "    "i" 
"  8  96  "   ";• 
"10120  "    ",' 
"12144  "    "i" 
M   6   8418505 
"-8112  ",  "i" 
"10140    "    ■"' 
"12168'  "    "i" 
16   6)'  9620546 
"•  8128   "i  "i" 
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"  12192  "    " " 
18   6 108 22 587- 
"!  8144  ",  "i" 
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"il2216'  "i  "i" 
20  6 12024 028- 
"I  8160  "I  "i" 
"10200  "    "," 
"  12240:  "I  "i" 


-1' 


— 1' 


12123 
"174 
"224 
"  274 
14133 
"164 
"214 
"264 
"304 
16143 
"  154 
"194 
"244 
"294- 
18194 
"    I  "214 
"264- 
"    I  "315 
I's  20204 
"    ,  "204 
"    !  "254- 
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l's22204 
"      "204- 
"       "244— 
"       "285 
I    ,,  24204 - 
"    i  "204 
"    !  "234 
"    i  "275— 


1 

-  Jsl 
-1      1 

-  ="4! 

-  -'41 

-  ^1 
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-  ^41 

-  ^1 

-  ".1 
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1    12 

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l'^3. 

II  s3, 

■  J«3. 
1     |3 
1'.3 
l's4 

s3. 
1  14. 
lVs4, 
13-8  4. 


.9817714 

.1020616 

.2724019 

.4827822 

.2622319 

.3726021 

.5629624 

.7833627 

00:?8131 

SI  23 

.0.   >1926 

.88  35729 

.1040332 

.3745237 

.3538834 

.5545638 

8450442 

.0855946 

.8249142 

.9854044 

2558948. 

5064753 

3257249. 

4762452 

7467756 

02  74561 

8866258. 

0572461. 

3077665. 

6084270. 


.6  9.4  1250    125 

.9  15.7  2060  206 

.7  23.2  3050  305 

.9  32.0  4220  432 


1  13.5  1800  LSO 
.3  21.2  2800  280 

3  30.6  4050  405 
.6  41.5  5500  550 
.1  53.5:  7100  710 
.8,  16.5  2200  220 

2  25  8  3400  340 
2;  36 . 5  4800  485 

.9  52.5:  7000  700 
.1  64  0:  8500  850 
.3i  40.0,  5300  530 
.5^  55.0  7200  730 
.8   72.0   9600   960 
9  91.0121001210 
2,  49  0|  6500  650 
.  4!  64  0-  8500  850 
.4  84.0111001110 
7106.0140001400 
4j  60.0,  8000,  800 
8  66.0  8800  880 
0  99.0131001310 
8122.0162001620 
71  71.0  9400  940 
2!  93.0123001230 
4117.0155001550 
2144.0191601910 


\iL^i 


**feti^.^aasP!R-=!5£ffiit^^r  •''-swi^as- 


COSCRFTF.    CVWERTS   AND    TRESTLES.     209 

TABLE  IX— Continued 

REINFORCED  CONCRETE,  SINGLE  BOX,  RAILROAD 

CULVERTS-BEAM  AND  SLAB  CONSTRUCTION 

TO  ACCOMPANY  FIGURE  45 


10  ft.  Rank  15  ft.  Dsnk.l^O  ft.  Rank.'so  ft.  Rank.!  40  ft.  Rank. 


M  ^  Jl 

s  *  s  „• 

?  S  S  I 

Ji  i  Js  c 


c 


6    'i 


27  535 

2.^  656 

25  820 

42  735 
36  816 

30  895 

! 

40  940 
'  34  1005 
!  28  1085 

i 

.  .'■  

40  1170 
34  1230 
28  1300 

31  1590 
25  1690 

\'\   '" 

30 
28 
28 

....1 
1920 

.... 

2i80 

25S0 

57 
51 


973  87 
1066  81 
45  1190;  75 
39  1317  69 
55  1230  85! 
49  1320!  79 
43  145..,  /3 


37  1570 

31  1675 

55  1530 

49  1620 

43  1735 


67 
61 
85 
79| 
73 


37  1910  67 
31  2000|  61 
46  2110  76, 
40;  2270  70 
34  2420 
28  2520 
45  2550 
39  2570 
33  2700 
27,  2850 
43  2920 
37:  2830 
31  3050 
25  3160 
43  3460 
37  3500 
3i;  3570 
251  3660 


64; 

58; 

75 

69 

63 

57, 

73 

67 

61 

55; 

73i 

67 

61 

55 


«» 

A 

» 

Xi 

1 

a 

s 

o 

1403 

1566 

1775 

2002; 

1800| 

1960 

2175 

2400 

2610 

2240 

2500 

2605 

2900 

3110 

3130i 

3430; 

3710 

3920I 

3810 

3900J 

4080 

4450J 

4400 

4410 

4720! 

£020| 

520O1 

5330I 

55361 

576(^ 


50  ft.  Rank. 

147  2283  1 
141  2576  2 
135:  2955  3 
129  3372  4 
145  2940  .'> 
139  3230,  6 
133|  3625  7 
127;  4050  8 
121  4510!  9 
145  367010 
139;  398011 
133  435512 
127:  485013 
121,  535014 
136  5180,15 
13f  .-,73016 
124  626017 
118j  671018 
135  6350:19 
129,  6550,20 
123  703021 
117i  7650122 
133|  7350;23 
1271  •'530,24 
1211  806025 
115i  872026 
1331  8740:27 
127  8980,'28 
121,  945029 
85  78601  115  991030 


117  1843 
111  2076 

105  2365 
99  2692 

115  2360 

109:  2600 

103;  2905 

97]  3220 

91  3530 

115  2950 

109  3190 

103  3485 

97  3870 

91  4210 

106  4150 
100  4580 

94  5000 

88  5310 

105  5070 

99  5250 


93 

5610 

87' 

6050 

103! 

5850 

97 

5980 

91 

6410 

85 

6870 

103 

6950 

97 

7180 

91 

7450 

f 


i^ 


:io 


coxcREiii  HRinci.s  .i\n  cii.rnRis. 


TABLE    X 

REINFORCED  CONCRETE,  DOUBLE  BOX,  RAILROAD 

CULVERTS     BEAM  AND  SLAB  CONSTRUCTION 

TO  ACCOMPANY  FIGURE  45 


H 


It 


1'  i'S 


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10    100      " 

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..   .1               n 

10 

4      SO    15 
0    120      " 

14 

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7 

S 

-. 

S    100     •' 

10  2;)o    " 



0 

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Silk'.'*. 


IVr  l.iti.  I'. 


12 


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20 


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174 

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224 

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27  4 

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i:{;{ 

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405   SS  (» 

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440   SO  S 

214 

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2.91 

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767   65 . 5 

214 

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940   SO  7 

20  4 

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s 

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911    7S  2 

20  4 

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254 

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1024   SS.O 

29  5 

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6 .  SO 

loss   94.0 

204 

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6.25 

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11. SO  97  0 

24  4- 

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6.95 

1195102  5 

28  5- 

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8 

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126S 109.2 

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1251  109  0 

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S.IO 

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27  .5- 

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1467126  5 

24   204— 


cosch'i/n:  cri.riiNTS  .i\n  r rustles. 


•11 


TABLE  X— Continued 

REINFORCED  CONCRETE,  DOUBLE  BOX,  RAILROAD 

CULVERTS  -BEAM   AND  SLAB  CONSTRUCTION 

TO  ACCOMPANY  FIGURE  45 


:'  r.irtiii. 


'lOft.Bank.'l.Wt. 


RHiik. 


20  ft.  HBiik.  nofl.  Rank.  40  ft.  Unnk.-V)  ft.  Hank. 


••■=•••£ 


■'    ^  .5    '      —     c     — 


^        *►        —        '-^        — 


14  :<   HMO 
•_'.>  (1  ;{(MK) 

;i2  4  4;UK) 

l:!  0  oTCK) 

.'(1  4  2720 

;il  .-)  42(K) 

4:{  2  .')72() 

.-,:{  .-)  7  UK) 

72  0  ».")(«) 

•Jii  0  :U.")0 

:{,s  c.  '>1(M» 

.Mr:.  7 KM) 

7;{  ()  !»7(M) 
.S7  0  11»)0 
.-.4  (t  7200 
71  0  94(h) 
!t|  (112100 
111   ()147(M) 

I      72  (I  \nm). 

5  02  012200 
117.015:)00| 
14H  0190001 

91  012100j 
10.-)  013900 
145  019200J 
Ho  023200 

9S.  013000; 
142  018800 
17(i  023400 
211.028100 


101 

3(K) 

430 

r)70 

272 

420 

572 

710 

950 

345 

510 

710 

970 

lUi 

720 

940 

1210 

1470 

960 

1220 

1550 

19(K); 

1210 

1390 

1920 

2320 

1300' 

18S0 

2340 

2810, 


27  915 


1(H)  I 


251450 


42 

3() 
30 

40 
34 

28 


40 
34 

28 


1350 
1380 
1440 

1590 
l(>(i() 
1(592 


2075 
2140 
2170 


31 


2750 
2700 


57 
51 
45 
39 
55 
49 
43, 
37i 
31! 
55 
49 
43 
37 
31 
4() 
40i 
34 


1720  87 
18701  81 
1940  75 
20401  69 


30  3310 


28  3810 


2S  4350 


28 
45 
39 
33 
27 
43 
37 
31 
25 
43 
37 
31 
25 


2082 
2200 
2292 
2340 
2520 
2785 

2 !»()()' 

2950, 

3090 

30701 

3720! 

3760i 

3760| 

3720! 

4480' 

4420, 

4450! 

4430 

5210 

4960 

5100 

5050 

6000 

6090} 

6040 


85: 

79 
73 
67j 
61 
85 
79 
73 
67 
61 
76 
70 
64 
58 
75 
69 
63 
57 
73 
67 
61 
55 
73 
67 
61 


2530 117| 
2750111 
2940,105 
3180  99 
3072115; 
3280109 
34921031 


36(50 
4020 


59701  55 


4105115 
4310109 
4510103 
4790J  97 
49201  91 
5(580106 
5890100 
60101  94 
6120'  88 
6860 105 
6S70  99 
7050:  93 
7250  87 
8010 103 
7890  97 
8170  91 
8320  85 
9250103 
9480  97 
9590  91 
9760  85 


4140 

45(>0 

4940 

5490 

5022 

5470 

5892 

(5310 

7050 

674510 

71(5011 

7(5(5012 

817013 

8(5(5014 

962015 


3330147 

3(550141 

3940135 

4320129 

4040  145 

1370139 

4692133 

.5010127 

5550121 

5445 145 

57601391 

6060  133J 

6480  127i 

67(50  121| 

7640136 

80001301014016 

82301241051017 

8520118  1092018 

92101351156019 

9321)1291182020 

97001231235021 
100501171290022 
108101331351023 
107901271369024 
113201211432025 
116201151482026 
1250013315X0027 
129801271638028 
132401211674029 
135101151731030 


:| 


I    J 


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■rf^sfSfivi.:  :«^..-yr  a.*!*!? ^'^ ■  s^.^; ;:^!§^i£*% 


COS-CRRTi:    CrUl-RTS    JXD    TRESTLES.      213 


X 

r. 


Cost  of  Reinforced  Concrete  R.  R.  Culverts. 

Singli'  Track  Banks. 

For-i-  kvctaijgiUar  Box. 

BrtHf  Pricfx. 

('i)iicrfte  ill  place  $H.OO    cr  yd. 
Steel  in  place  4c  per  lb. 


Jo'         too  I  So 


Fig.  46. 


j^"i'- 


til 


i.i 


I:'': 


^■i 


i 


ll'llil 


I:       i 


lU 


COXCRETIi    BRIDGES    .WD    CriAT.RTS 


(lonhio  or  singlo.  Culverts  of  these  forms  cost  less 
for  ixny  given  area  than  if  made  with  ,vi(ler  ami 
shallower  openings.  The  reason  for  this  is  due  to 
the  fact  that  for  wider  openings  the  thiekness  of 
.•()V(>r  slabs  increase  more  rai.idly  than  the  thickness 
of  side  walls. 

From  the  comparative  cost  chart.  Figure  4fi.  the 
follov.ing  conclusions  are  deduced: 

Single  box  slab  culverts  are  economical  for  areas 
up  to  50  sfpiare  feet. 

Double  box  slab  culverts  are  economical  for  areas 
up  to  7")  s(|uare  feet. 

Single  box  beam  and  slal)  culverts  are  ecoiu.mical 
for  areas  up  to  12.")  .s(|uare  feet. 

Doul)le  box  beam  and  slab  culverts  are  economical 
for  areas  above  125  square  feet. 

Wide,  flat  culverts  cost  somewhat  more  than  nar- 
row and  higher  ones  of  the  same  area,  but  they  are 
nu>re  effective  ami  offer  less  resistance  to  the  free 
flow  of  water.  For  a  bank  of  any  given  height,  the 
loAv  culvert  will  have  a  longer  barrel  than  a  higher 
one.  though  this  will  be  offset  to  sonu'  extent  by  the 
sh(nner  length  of  wing  walls.  There  is  little  or  no 
economy  in  reducing  the  length  of  culvert  barrel  by 
using  high  end  parapet  retaining  walls,  as  material 
thus  used  might  better  be  employed  in  increasing 
the  length  of  culvtit  barrel,  thereby  causing  shorter 
wing  walls. 

Tn  proportioning  the  thickness  of  wing  walls, 
M  h(  n  these  wings  are  placed  at  a  considerable  angle 
to  the  culvert  face,  the  stability  of  the  wing  wall  is 


"^1% 


mjsmm^'^-^'^ssm^ 


COXCRL    E    CULILRTS   AXU    I  RUSTLES.      215 

11u'rel)y  jjrcatly  iiKToasod.  and  it  is  fronorally  safe  to 
make  tlie  l)a.se  thickness  of  the  ■\viiigs  near  their 
('((iiiieetion  to  the  tnient  from  20/^    to  2y/(    of 

the  Aving  wall  heijrht.  Towards  the  ends  wiiere 
the  wings  reeeive  no  support  from  the  eiilveit 
sides,  the  width  or  thickness  of  wing  wall  base 
should  then  be  40%  of  the  unsupported  height. 

The  size  of  beams  and  slal)s  given  in  Tables  VIF, 
\'1II,  IX  and  X  are  for  culvert  barrels  sul)jected  to 
the  loads  specified,  which  occurs  at  and  near  the 
eenter  of  the  embaidiment.  For  long  culverts,  thest; 
sizes  may  be  rediu-ed  towards  the  ends  where  the 
loads  are  somewhat  less  than  at  the  middle. 

^Vhere  the  nature   of  the   soil   will   permit,  some 
economy  nujy  result  by  omitting  the  reinforced  con- 
crete  pavement   slab,   and   r.ubstituting   ot^'set    foot-' 
ings  under  the  side  walls,  as  shown  on  the  concrete 
trestle    plans.   Figures   aS   to   (io    inclusive,    using   • 
cobble  stone  pavement,  if  recpiired. 

There  is  less  probability  of  debris  and  drift  col- 
lecting when  the  culvert  bottom  is  curved  or  disheil 
out  at  the  center,  than  when  built  flat  or  horizontal 
bctAveen  the  two  side  walls.  Hox  culvert  corners 
should  be  l)ra('ed  with  straight  or  ciu-ved  c(»rn(>r 
fillets,  reinforced  with  diagonal  rods,  as  shown  on 
tile  tyjiical  drawings. 

Tt  is  unnecessary  to  increase  the  thickness  of  side 
walls  from  the  top  to  the  bottom,  excepting  perhaps 
for  high  culverts,  and  eveii  tlicn  '^inep  tlic  condition 
of  earth  pressure  on  the  side  walls  is  uncertain,  any 
efTort  at  ultra-refinement  is  unnecessary. 


216 


COX'CRIiTE    HRimmS   AM)    CCLIHRTS. 


"Walorproofiiij,'  slioiild  be  used  on  the  exterioi' 
surfaces  of  the  roof  mid  sides  to  provont  drainage 
■water  from  soakinjjj  into  the  eoiierete.  Tlie  ad 
hosion  of  eoncrete  to  steel  is  decreased  about  IOC 
when  the  eoncri'te  is  eontinnously  water  soaked, 
and  this  decrease  can  l)e  avoided  by  finisliing  the 
outer  surfac(>  of  the  top  and  sides  with  a  coating  of 
neat  cement  or  otlier  waterproof  material. 

Comparative  Costs  of  Culverts  of  Various  Forms, 
Figure  47  shows  the  comparalive  costs  of  reiid'orced 
eoncrete  box  railroad  culverts  compared  Avith  corre- 
sponding costs  of  culverts  of  other  forms.  The 
chart  gives  the  total  cost  of  culverts  for  an  end)ank- 
ment  20  feet  in  heiglit.  and  for  cross-sectional  areas 
varying  from  .")  to  200  s((nare  feet. 

The  new  reinforced  concrete  l)ox  culverts,  the  co-it 
of  which  are  shown  by  the  heavy  line  nund)er  10, 
are  more  economical  than  any  other  jx-rmanent  cul- 
verts, and  cost  but  little  more  than  wooden  l)ox 
culverts.  They  rangi-  in  cost  from  'M)  to  oO  cents 
l)er  s(|nare  foot  of  sectional  area. 

The  various  culverts,  the  costs  of  whicli  ai-e  shown 
in  Figure  47  by  lines.  ar(>  as  follows: — 

Xo.  1  srives  the  cost  of  standard  cast  iron  pipe 
culverts,  which  are  suitable  only  for  small  oi)enings, 
and  while  they  can  l)e  quickly  placed,  and  some- 
times inserted  inside  of  Avorn-out  temporary  wooden 
box  culverts,  they  are  not  economical. 

Xo.  2  are  reinforced  concrete  box  culverts  with 
bottoms,  similar  to  those  in  use  on  the  rnion  Pacific 
and  Southern  Pacific  railroads. 


W^^^^*^ 


'a.:.*,^ 


'«i^i,a*«....,i;'#-*-: 


'■■'■^^■: 


coxCREiE  cn.rr.RTS  .ixn   ihT.srij-s.    217 

Comparative  Costs  of  Culverts. 

STNGLK   TRACK    RAILROAD.      IIKIGIIT    OK    HANK    20    IKKT. 

,    1  Cast  iron  pipe. 

2  Reinforced  concrete  box,  witli  bottoms. 

H  Kali  top  concrete  box. 

4  Reinforced  concrete  iirch. 

5  Solid  concrete  arch. 

6  Stone  arch,  Baker's  standard. 

7  Reinforced  concrete  box,  no  bottoms. 
H  Rubble  stone  box. 

9     \V<M)d  box. 
It)    Reinforced  concrete  box,  new  standard. 


t 

:      yzzz: 

J 

T"                         y 

1                             ''                  &■■! 

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*^7.2" ' 

_i^-  _  ii":                                              :. 

Tor  St.    A^m/t    00  Wifrg/rwitY. 

Fig.  47. 


/So* 


ZOO 


Ain-     .   "iti'S'-:-- -  W'-'^  "■■■ 


i  I 


'  I  i 

Ml 


M 


11 


il, 


21^      coxch'i-.Tn  BRincis  .ixn  cri.rr.RTs. 

\().  ;5  iifc  coiicrctf  rail  lop  <mi1  verts  lijiviii«r  slabs 
J.")  1(»  IS  iiiclics  thick,  find  reinforced  with  rails 
spaced  IS  inches  apart  for  a  O-foot  span.  10  inches 
apart  for  an  S-foot  span,  and  C>  inches  apart  for  a 
lO-foot  span. 

Xo.  4  are  reinforced  concrete  arches,  similar  to 
lliose  in  iis<'  on  tin'  ahove  named  railroads. 

Xo.  T)  are  concrete  arches  withont  reinforcement. 

Xo.  f)  are  se<;mental  stone  arcli  culverts  as  pro- 
posed by  Mr.  IJalvcr  in  his  book  on  ^NFa.sonry  Con- 
stiMiction. 

Xo.  7  are  reinforced  concrete  box  culverts,  similar 
to  Xo.  2.  exceptinjr  that  they  are  without  bottoms 


2:— Portals 

(JoiiiTrtf  72  yds.  ii  ♦«.()()-  $576 
Steel     a450  lbs.  (</      ,01        \w 

»714 
Barrel  per  Un.  ft. 
Concrete  itiMyda.  iii(  <;s.(M)-  ♦ll'i 
Steel         45»»lbs.  (i(      .04       IKO 

♦.''SI 
Length  for  20  ft.  bank    -  32. 
Area  -^  180  aq.  ft.     Cost  |i24a0. 


t'lg.  4tt. 


CONCRETE    CCI.rERTS    .l.\l>    TRESTLES.      219 


and    cost    proportionately    loss.     They    have    offset 
footings  under  the  side  walls. 

No.  8  are  rubble  stone  box  eulverts,  the  kind  most 
eonnnoidy  used  by  the  railroads  until  recently,  for 
small  openings. 

No.  0  are  wooden  box  culverts,  and  while  they  are 
not  permanent,  they  have  the  merit  of  being  the 
least  expensive  of  all. 

No.  10  are  the  new  standard  reinforced  concrete 
box  culverts,  as  shown  in  Figures  43,  44  and  45, 
Ihe  quantities  and  cost  of  which  are  given  in  Tables 
YII,  VIII,  IX  and  X. 

An  actual  cost  record  for  building  a  4-foot  con- 
crete arch  culvert  under  a  railroad  embankment  in 
Idaho,  during  the  tliirty  days  from  June  oth  to  July 
J  1th,  1003,  is  as  follows:— 

Foundations  contain  111  yards,  and  cost $5.00  per  yd. 

Upper  part  contains  137  yards,  and  cost 7.00  per  yd. 

Average  cost  about  G.OO  per  yd. 

Cost  of  whole  culvert  per  cu.  yard  of  concrete.  10.00  per  yd. 

Portland  Cement  used,  272  barrels.    Cost 2.70  per  bbl. 

Foreman   paid $150.00    per    month. 

1  Finisher  paid 3.00  per  day 

Laborers    paid 2.00  per  day 

4  Carpenters  paid 3.00  per  day 

Labor  cost   $1723.00 

Alaterial    cost    830.00 


Total    $2553.00 

Concrete   made   entirely    from   sand   and   gravel   at   rail- 
road company's  pit,  without  any  broken  stone. 

Other  Common  Culvert  Forms.    Figures  48  to  57 
inclusive,  show  other  forms  of  culverts,  and  Table 


II  '. 


■ 


\  \ 


lii 


220 


COXCRETE   BRIDGES   ASD   CilA'ERTS 


XI  contains  their  ostiniated  quantities  and  costs. 
For  the  purpose  of  comparing  these  with  others,  the 
costs  have  been  estimated  for  lengths  re(iuired 
under  a  20-foot  embankment,  and  these  costs  are 
given  in  Figure  47,  together  with  their  correspond- 
ing numbers.  They  vary  in  cost  from  2G  to  36  cents 
per  scjuare  foot  of  section  area,  for  each  lineal  foot 
of  culvert. 

Figure  48  is  a  reinforced  concrete  boxcidvertl2 
feet  high  and  15  feet  wide,  v'th  rod  reinforcement, 
similar  to  the  new  single  box  slab  culvert.  For  so 
large  a  section  area,  the  slab  typj  is  not  economical. 

Figure  49  is  a  reinforced  concrete  box  culvert  of 
combined  beam  and  slab  construction.  12  feet  high 


1^  ''t-i 


2  Portals:— 
Concrete  74  yd8.(i?*8  (X) 
Steel      472U  lb».  <tt     .04  -- 

Biirrelperft. 
Concrete  5 .  K  yds.  (ft  $H.(in 
Steel        615  Ibs.fe    .04-^ 


'Dgthfor  20  ft.  bank 
Area  -230  square 
CdRt  =  $2<)3(). 


-1592 

=    188 

»780 

$4r4 

=  20.6 

*67.6 
=  32  ft. 
feet. 


Fig.  rj. 


CONCRETE    CrU'ERTS   .IXD    TRESTLES.      221 


and  20  feet  wide.  For  an  area  of  this  size  a  more 
C'cononiieal  form  is  secured  by  using  a  double  box 
of  the  same  general  tvpe. 

Figure  50  is  a  beam  top  culvert,  12  feet  high  and 
1.')  feel  wide.  The  culvert  top  is  arched  3  feet  and 
tlie  arch  strength  is  f'onsidered  when  proportioning 

'mm. 


2  Piirfals:— 
Concrete  88  yds.  ^  $8.00    f;704 

Barrel  per  lln  ft. 
Concretee.  1  yds.  (&  $8.0O=- 148.8 
Steel        240  1bB.fe    .04^    9.6 
t68.4 

Length  for  20  ft.  Bank^-32  feet. 

Area      161  sq.  ft.     Co8t  =  |2570. 


FIk-  5lt. 

tlie  thickness  of  the  culvert  top.  Culverts  similar  to 
this  have  been  used  by  the  Illinois  Central  Railway 
Company. 

Figure  51  is  a  concrete  box  culvert  with  rod  rein- 
forcement similar  to  Figure  58,  excepting  that  in 
it  offset  footings  and  cobble  stone  pavement  are 
used  instead  of  a  reinforced  concrete  pavement  slab. 


1 1 


I 


i(>Xii\'fiii:  liRiinns  .r:i>  crirnRTs. 


t   Ourwvfn 


i  ro^ 


■1  Forliils:    - 
Concrete  88  yd*.  ^  |S.00    *704 

Barrel  per  lln.  ft. 
Coneretee.ayrlH.  (fi  »s  (X)    ♦49.0 
Steel        150  Ihn.  lit      ,04         ti6 
♦•Vi  6 

If  foandntinn  l>t  depresneil  in 
own  dotted,  then  area  —  173 
iiare  feet. 

Leritflh  for  20  ft.  bank=3a(t. 
St      |24»'U. 


Fljf.  r.i. 


Fi<ji:ui"('  r)2  is  a  roint'orced  coneroto  box  enlvort  of 
ht'iim  and  slab  oonstruetiuii,  12  feet  high  and  20  feet 
wide.  For  so  largo  an  area,  a  donble  box  of  the 
same  type  "vvill  be  more  eeonomical. 

Figure  53  is  a  culvert  of  the  same  dimensions  as 
Figure  52,  Avith  solid  conerete  side  walls,  l)ottoni 
cobblestone  pavement,  and  roof  reinforced  with  dou- 
ble lines  of  60-pound  track  rails,united  with  %-inch. 

Figure  54  is  a  reinforced  concrete  arch  culvert 
with  buttressed  sitlo  walls  and  slab  pavement. 
Structures  similar  to  this  are  used  by  the  Northern 
Pacific  Railroad. 


cnxcRFTi:  criiTRTs  .\\n  tri-stiis. 


(Jl  ANJITIKS 

(;i.iiiri>tHn3y>l-.»»  IS.IXI  IW"* 
Steel  14500  \\>*.  <«  .04  SW" 
$11M4 
Uiirrel  per  lln.  ft. 
('i.n<T(,tB4.«yd»."<»s.0O  fM.H 
StffI         7("l  Ibx.  (c(       04       'J8  0 

LeiiKlli  for  20  ft.  biink-    'rifl. 
Areu      ■J40«(i.  ft      Oost*3100. 


Fi<riir(>  .").")  is  ii  l)ciuii  top  culvrt  12  feet  liigli  iiiitl 
Hi)  i'tH'l  wide,  similar  to  Fit^iin-  .')().  It  will  !»»'  sceii 
that  neither  of  these  types  are  eoononiieal. 

Fijjure  .")()  is  a   paral  'die  aicii  culvert. 

l'M<rure  ill  is  a  icinroreed  eouerete  areii  culvert 
possessiiifr  jjreater  merit  than  any  other  form  of 
arch  culvert  now  in  use.  It  contains  the  least 
amount  of  material,  the  saving;  hein«;  chiefly  in  the 
sides.  :\ias(»nry  arch  culverts  of  the  old  type, 
whetlier  huilt  of  st(.ne  or  concrete,  have  the  greater 
l)art  of  their  material  in  the  side  walls  or  ahutmcnts. 
Fi<:;ure  'u  is  designed  similar  to  a  tunnel  center,  or 
a  sewer  arch,  and  its  form  and  light  eonstruetiou 


w: 


lii 


llit! 


i  I 


2l'» 


loxck'inr.  lih'/nar.s  .ixn  cn.rr.RTS. 


art'  possible  (tiily  liccause  (»f  tln'  ((rcsoiifc  (tf  roin- 
forciiij?  metal  in  the  areli  riri^f.  Culverts  of  this 
p'lieral  form  are  heiiij;  used  hy  several  of  the  rail- 
road companies  antl  are  eeononiical.  They  have  n 
disatlvaiitafre.  however,  in  re(|uirin};  th(>  use  of 
enrved  forms,  hut  this  is  overcome  to  some  extent 
l)y  iisinj?  colla{)sil)le  centers. 

A  jHodification  of  tliis  form  of  culvert  using  a 
semicircular  top.  is  also  sliown  in  Fijrure  '>'. 

Mr.  Luten's  rules  for  proportionin<;  such  arches 
under  railroad  baidis.  in  spans  of  .lO  feet  or  less, 
and  with  a  depth  of  earth  filliuf;  above  of  not  less 
than   10  feet,  are  as  follows: — 

fVowu  TiPcluu'ss  0=.''^""'+.',. 

:5() 


2PortaN 
CotKT' H- SH  yds.  «<(  I8.1H)       1701 

lliirrf  1  jx-r  Ilii.  ft. 
Ciincrete  H  yds.  (ii  HH.dn      f6».(Ht 
Moel       1015  lbs.  fa  .015        ir>. •.>•.' 

etiRth  fur  20  ft.  liiiiik      30  ft. 
Area      'Jr.o  si|.  ft.     diHt  I30MI. 


FiK.  y-i. 


coxcRi  Ti:  Lr/.iiiuTs  .ixn   ii<i:siLiis.    225 

,,         HpHll 
hi  =-rr  -  . 

10 

Fiiick  (if  iiliiitiiictits  hnttcr  (mm'  in  four. 
Till'    mimluT    iif   sijiijiii'    iiiclu's    of    s\vv\    f(»r   oiio 
t'«I<,'<'  I»<'i"  litM'iil  foot  of  jircli  is 

}{  L 

40(».iM)(tl). 

li  is  tlif  live  load   in  pounds  lluil   ciin   Ik-  fonccn- 
tratcd  on  the  half  anli  for  on«'  track. 


■J  PiirtalH:— 

(Concrete  47  yilo.  »i  IH.OO 
Steel       1600  Ibx.  <>(       .(M 

Harrel  p»'r  ft. 

''(>ncret»3.1y(ls.  (fi  $H.(Hi 
Steel  ITli  11)8.  ^     .ot^  : 

.\reii      92  sq.  ft.  I,f'ii»rth  for 
bank       4'.'  ft.      i^n^l  for 
hank,  »17H0. 


♦376 
_fi4 
$140 

I-J4.8 
_6^« 

131.6 

20  ft. 
20  ft. 


±7-0^ 


Fig.  54. 


Illlll 


22fi      coNCRiirn  BRincEs  Axn  culverts. 


2  Portals:- 
Concrete  68  yds.  *<  iH.Od      t7()4 

Biirrel  per  ft. 
Cc>ncrete7.2.")  yds*. »/ $8.00  ^$58.0 
Steel  4fiO  lbs.  *(       .04      18.4 

LeriKth  for  20  ft.  bank  =-32  ft 
Area       •21.'-.  8<i.  It.     Cost  »3150. 


-....;.».  ^.,..J^    _\l   2  Portals:— 

U-V-V-ii-T-VH^^  -5f,      Concrete  4;<.4 yds. *»t8.r)  I    t3«7.'.' 
f.'. .'-'::; -irrl;—! — 4-     steel       2fi7(iib».r«     .u4     lofi.s 

t:.:  ;:::;-,».Ti  =3=  =4.  '""'■•■i i">r ft. 

tT'j-T.ii'fi".  -r-    ^""        f^onorete  3.3  yds.  *(  |8.(KI      |26.4 
Steel  230  lbs.  *(      .04  '^:l 

Are*  12«  scj.  ft.  I/enKth  for 
20  ft.  bank  :t'.tft.  (^ost  for '20  ft. 
blink,  tl8(4. 


FlK.  :,(,, 


/' 


COXCRETE    CULVERTS   .IXP    TRESTLES.      2L'7 

R  is  the  hoiijlit  in  feet,  ami  1)  tlic  crown  tliieknoss 
in  iiichos. 


Fig.  57. 

TABLE  XI 

CULVERT  DATA,  FIGURES  48  TO  66 


Harrpl,  iirr  ft. 

2 

Portals 

20  ft 

.  Bank 

^ 

r. 

•f. 

,1 

L 

^ 

2 

^ 

■~. 

t,  -^ 

c 
u 

S 

3 

t 

t.i  "* 

-r 

*f> 

it   "^ 

"^ 

S 

-< 

4.7 

■A 

— 

C  C^" 

•/. 

*. 

is 

1.-. 

12 

ISO 

4.-.0 

.■>:. .  4 

72 

34.-.0 

714 

32 

24S6 

30   ,S 

•!<» 

20 

11 

2:50 

."i.S 

..1.-. 

67.0 

74 

4720 

7S() 

32 

2924 

WW    1 

:>(! 

l.-) 

11 

161 

6  1 

210 

.is.  4 

HH 

704 

32 

2.'>72 

36  4 

51 

i:. 

11 

172 

6.2 

l.M) 

.V).6 

HS 

704 

32 

24S3 

3'  4 

:>2 

20 

12 

2 10 

4,6 

700 

64.  S 

113 

14,'.(K) 

14S4 

2."> 

3104 

27.0 

.l.'l 

■M 

12 

■JAI 

f(.U 

101:. 

79.1 

8,S 

704 

.«) 

.1077 

31    8 

.y\ 

10 

10 

92 

:m 

170 

31.6 

47 

16(K) 

440 

4'.! 

17S4 

31  4 

O.I 

20 

11 

215 

7.2 

460 

76.4 

SS    . 

704 

32 

3148 

3:> . .') 

M 

lU 

10 

128 

■A.i 

230 

,'ir>.6 

43 

2670 

4.-,4 

3<> 

1S44 

27.8 

;.l.""'.-' 


"!^^ 


t\ 


II      f 


228        COXCRETE   BRIDGES  JXD    CULVERTS. 

CONCRETE  RAILROAD  TRESTLES. 

Figurt's  ."58,  59  and  61  to  (io  inclusive  sliow  five 
different  types  of  reinforced  concrete  railroad  tres- 
tles. In  connection  with  these  and  for  the  purpose 
of  comparison,  a  diaj,'rain  and  table  of  dimensions  is 
j^iyen  in  Fij,'ure  60,  for  double  track  steel  beam 
bridfjes,  a  type  jrencrally  in  use  by  the  railroad  com- 
panies for  short  spans.  The  drawings  for  these  dif- 
ferent types  of  concrete  trestl(>s  show  double-track 
structures,  28  feet  wide  Avith  1.")  inches  of  filling, 
suflficient  only  for  the  usual  depth  of  ballast.  When 
headroom  or  other  conditions  will  permit,  additional 
space  for  earth  filling  beneath  the  ballast  shoidd  be 
provided,  making  *.  mininnnn  depth  from  base  of 
rail  to  concrete  of  not  less  than  :]  feet.  \n  many 
bridges  this  depth  has  been  exceeded.  The  arch 
viaduct  over  the  Santa  Aiui  Kiver  at  Riverside.  Cali- 
fornia, has  a  depth  of  ,1  feet  from  the  base  of  rail  to 
the  extrados  at  the  crown. 

These  trestle  designs  marked  A  to  11  inclusive  are 
of  the  following  types: 
Double  Track  Structures. 

A.     Kailtops.     Loads  carried  entirely  by  rails  in 
])ending. 

H.     Beamtops.     Loads  carried  entirely  by  beams 
in  bendijig. 

r,     Standard  steel  beam  bridges.     Open  decks 

D.  Reajjitops.     j.eams  for  reinforcing  only. 

E.  Reinforced  concrete.     Slab  type.     Ii(>d  rein- 
forcement. 


COXCRllTE    CVIJl-.KTS    .IXD     I  RnSTI.liS.      229 

F.     Kciiiforcpil    ('(Uicroto.      lioain    and    slab    type. 
IJod  I'cinf'orfeinent. 

SINGLE  TRACK  STRUCTURES. 

(i.     Reinforced   concrete.     Slab  type.     Kod   rein 
fdreenient. 

11.     Keiid'oreed    eoncrele.      IJeain    and    slab    type. 
Uod  reinforeeinent. 

These  standard  trestles  were  desijjfiied  by  the  au- 
thor, ^vithont  special  reference  to  the  standard  cul- 
verts, ami  also  under  a  sonunvhat  different  si)ecifiea- 
lioii.  Instead  of  making  an  impact  alknvancc 
amounting  to  '^O^/r  of  the  live  load  aiul  using 
a  7!>()-i)ound  concrete  working  unit,  as  in  designing 
tiie  concrete  cidverts.  the  stamlard  trestles  are  de- 
signed -with  no  impact  addition  and  with  a  working 
nnit  of  500  pounds  per  scuuire  inch  for  concrete  in 
iMMtiprcssion.  The  assiuued  engin(>  load  is  Cooper's 
1-)  .")(),  Avhich  is  e<|uivalent  Avhen  distributed  by  the 
ties,  rails  and  ballast  to  a  i>uiform  live  load  of  1,100 
|)ouiids  per  s(|uare  foot.  To  this  is  added  the  weight 
nf  track,  filling  ami  coiuu-ete,  nmking  the  total  loads 
fro;  .  l..")00  to  1.700  pounds  per  scpiare  foot,  as  par- 
■  .  'y  noted  on  the  various  ngiu'es.  The  founda- 
•  are  of  sufficient  width  so  the  bearing  pressur*^ 
(  e  soil  will   not   exce(>d   three   tons   per  scjuare 

foot.  For  the  i)urposc.  however,  of  making  the  esti- 
mates lil)eral.  the  pier  (putntities  in  all  cases  include 
l)iles.  It  will  ])('  scM'n  that  on  each  plate  is  a  table 
giving  the  length  of  span,  thickm'ss  of  concrete, 
size  of  metal,  and  the  (juantitios  of  concrete,  steel 
and  ballast,  together  with  the  estimated  costs  for 


•W 


if 
I! 


iiiil 


2;!0        COXCRIiTIi   BRUKiliS   .1X1)   ClLlllRTS. 

tlu.  various  spnns.  In  .....uuvtiu,,  with  .I.sifrns  |} 
•>.  K  juul  (J.  th.-n.  i,.v  als.,  tahLvs  jrivin-  tl„.  sizes 
;i'"'"ftH-s  and  ,.osts  for  ,,i,M-s  of  various  heights 
"'"  I"<''-s  vary  fron,  2  t..  ;5  f.vf  i„  thiHou-ss  at  the 
"!'•  'I-P«'n.lu>-  o„  their  hei^^ht,  an.l  thev  have  si,!.- 
'•'tt-rs^  of  1    i„  24.     AVhen  piers  have  a'less  height 

'''"l->  f-t.  Ih.re  is  only  a  single  fooling  eourse  Hi 

<'"•  l>Hs<..  1,ut  for  heights  greater  than  i:.  fe,.t  there 

■'•••'  2  tooting  eonrses.     This  is  neeessary  to  prevent 

I'"   load   on   the   soil   ...xeeeding  :{   tons   j.er  square 

root. 

Economic  Span  Lengths.     The   designs  are   made 
••'•spans  up  1o  :.4  feet   in  length  and   piers  up  to 
•^"  /!'•'♦    '"    l"M^d.f.   and   are   suitable   f,,,-  struefures 
"•■th.n   these   li.nifs.     TIh>   eeonon.ie  span    length   to 
iise  tor  any  given  heiirht  of  tn-stl..  is  that  one  where 
tlH"  eost  ol    the  span  i.  approxin.afely  equal  to  th.' 
-stofp.er.     Th,.  ,.ost  of  pi.r  f.,,  the  given  trestle 
l'"'jrl.t  n.ay  he  taken  direetly  from  the  pier  tables 
and  tn.m  the  .'orrespon.ling  table  giving  the  eost  of 
■si>an,  a  length  nu.y  be  sele.-ted.  the  eost  of  whieh  is 
;'PIH-oxnnately  e.pud  to  the  eost  of  the  pier      ir,v 
H.g  thus  d.-tennine.l  the  eeonon.ie  span  length    ihe 
various  sizes  may  i>e  tak.Mi  Jireetly  from  th..  tables. 

Description  of  Various  Trestle  Designs. 

The  following  are  brief  deseriplions  of  the  various 
trestle  d.'signs  referred  to  ai)()ve  — 

Design  A  Figure  58.  This  is  a  type  that  has 
»>.-.>n  extensively  used  for  small  spans  up  to  12  feet 


'  «&"  'HUV^'tMMt  '?-)kIl&r«^' 


j: 


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232 


COXCRETE   BRIDGES  AND   CULVEkTF. 


m  length,  tliough  usually  restricted  to  a  length  of 
8  feet.  The  loads  are  carried  entirely  by  the  bend- 
ing resistance  of  the  rails.  Railr-^'ad  companies 
usually  have  a  large  stock  of  old  track  rails  on 
hand,  which  they  are  willing  to  sell  to  their  con- 
struction department  at  a  price  of  from  $20  to  $30 
per  ton.  They  are  estimated  in  the  table  accom- 
panying Figure  58,  to  c.»st  $40  per  ton.  or  2  cents 
per  pound,  placed  in  position.  Only  a  sufficient 
thickness  of  concrete  is  used,  to  completely  embed 
the  rails  and  hold  them  securely  in  position.  The 
strength  of  the  concrete  is  considered  onlv  by  allow- 
ing a  flange  stress  of  10,000  pounds  per  scpiare  inch 
on  the  metal,  which  is  20  per  cent,  greater  than 
would  be  permitted,  if  the  concrete  filling  were  ab- 
sent. This  type  of  bridge  is  going  out  of  favor,  not 
only  because  it  is  not  economical,  but  also  because 
there  is  no  provision  for  resisting  shearing  stresses. 
Bridge  decks  so  constructed  have  excessive  deflec- 
tion, and  the  concrete  frequently  cracks  and  'jlls 
away  from  the  rails,  leaving  the  steel  exposed. 

If  loads  were  carried  by  the  bending  resistance  of 
the  concrete  and  rails  used  only  for  the  purpose  of 
reinforcement,  these  rails  would  then  be  spaced 
from  2  to  3  feet  apart.  The  best  modern  practice 
in  the  use  of  railtop  trestles  and  culverts  is  to  adopt 
a  mean  between  these  two  extremes,  and  use  slabs  of 
concrete  IS  inches  in  thickness,  reinforced  with  old 
60-pound  rails  spaced  as  follows : 

For  6- foot  span,  place  rails  18  inches  apart  on  cen- 
ters. 


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Foi-  lO-l'odt  span  |tliif(>  rails  (i  iiiclics  apart  on  ccii- 
Icrs. 

Design  B.  Figure  59.  Tn  Ihis  design  beams  arc 
placed  1.")  inches  apart  on  oonters,  and  are  snf- 
liciently  heavy  to  carry  the  entire  load  by  the  beiid- 
inj,'  resistance  of  the  beams.  No  reliance  is  placed 
upon  the  concrete  except in<?  that  a  workinj?  fibre 
stress  on  the  metal  of  12.000  pounds  per  sijuare  incli 
is  assumed,  wliich  is  greater  than  would  be  used,  if 
the  concreto  were  absent.  Tho  beams  are  firmly  em- 
bedded in  concrete  "with  a  minimum  thickness  of  ■) 
iiKdu's  beneatli  the  beams,  and  a  similar  depth  of 
concrete  above  the  beams  at  the  gutter.  The  upper 
surface  of  the  concrete  slal)  is  sloped  from  the  gut- 
ter up  to  the  eenter  sufficiently  to  drain  the  water 
to  the  gutter  and  i)revent  it  from  soaking  into  anil 
disintegrating  the  concrete. 

Design  C.  Figure  60.  There  is  no  conerete 
whatever  in  connection  with  this  design.  It  is  one 
of  the  conunon  forms  of  sh()rt-si)an  railroad  bridges. 
aM<l  the  table  of  sizes,  weights  and  estimated  costs 

is  given  for  comparison  Mith  tlu st  of  reinforced 

concrete  designs.  The  tyi)e  of  bridg(>  is  inferior  to 
the  concrete  designs  because  of  their  open  decks. 
An  ojM'ii-deck  bridge  is  a  weak  place  on  a  perma- 
nent roadway.  Tf  a  train  is  derailed  on  a  solid  deck 
liridge,  the  chance  of  injury  either  to  the  train  or 
structure  is  less  than  wlien  derailment  occurs  on  an 
open  deck  bridge. 


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l><'sit?..  15,  but  (HHVrs  from  it  in  hiivin^r  a  suffi.-i.  nt 
tlii.-kiU'SM   „f  ,-.,n.-.vt(      nM,ir,„vnl    uiti,   Strrl    l,,-;,,,  . 
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Ih,.  b.w...-  tv  ,;„!,...  ,,Mly  of  tb..  st.'.'l  bi.a.M.  arv 
'''■  '  I  'iisi  11  iiu'tal.  for  .•.aicn-to 
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t'oiiiMu  iIh.  tbi.ku.-ss  of  I,.,  sl.-u.s  tb..  otr.'.-tis  ■  spat. 
l<'M-tIi  IS  assn,n..,I  .„,..  fo.>t  slu.rt.T  tban  fbo  a-Mial 
l"*«'mis(.  .»f  til.   i.n.s..n.-(.  .)f  •  u-s,^  (•..rb..ls. 

Design  E.     Figure  62.     Tl.is  is  a  r.-i,  r.„v..,l  .on- 
on.t..  tr..stb.  (b-sio.,,,  hotb  span  an.l  pi.-rs  havi..-  rod 
r.-int..r<...monl      I„    tb..    two   pr.'vious      '   ,    ,l,.sij?ns 
r..infor.-iM<,'  st.-,.]   is  ..i,iitt<.cl.  I  ut   for  D-'si-n  E  ."n.-- 
lu.lf   in.'b   s.niarc   n.  Is   a.v   ph..    d    \^   in.-l,..s   apart 
botb   bnnz.>iitally  an.l    vcrti.-ally       Tb-      r...ls  serve 
not  ..nly  t..  pro\..nt  .-racks  fr,.,,,  .•bati-..     f  t.-.Mp.Ta- 
tnr..,  1),it  als.)  r..sist  any  t.-nsi!..  sln-ss.  .  -.vbi.-b  nii-bt 
omir  in  tbin  pi.-rs.  .In.  t,»     ■„    -u.Mcn  st..i,pinK''ol 
1.   .vy  trains  ..n  tb.'  bri.li,,..     Tb.   spans  ar..  sl.!b  con- 
stnir-tion.   witb   a    10-in.-b   slab    f.)r   t;-fo.)t  span,    ii- 
croasinjr  to  3(;  Jnclics  f.)r  a  24-foot  span. 

Design  F.  Figure  63,  I.ik..  ,i„.  pn-vious  -n. 
tbis  .l.^si.irn  is  r.Mnforvo.l  ..ntin'ly  with  ro.is.  l,ut  is  a 
(•.MHl)inati.)n  ..f  boa  a  and  slab  .•.,nstnifti..n  Lon'W- 
tmluiMl  ,...n<-r..t.  b.ai.s  .n  p]a..-d  0  f,-,.,  apart  In 
the  .-b-ar.  and  to  tb<^s,.  loa.is  an  ransniittod  hv 
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track  nn.I  l.Mllj.st.  TIh-  si.I,.  beams  aiv  oacli  2  feet 
III  Avidfli.  while  tlie  center  l)ea.n  is  4  feet.  The  load 
IXT  lineal  f<M,t  ..n  llie  side  beams  varies  from  8  ofV) 
pounds  for  a  lO-foot  span  to  n.:JOO  pounds  for  a  24- 
ioot  span. 

Designs  G  and  H.     Figures  64,  65.     Th,-se  a.v 

dcs.jrns   for  sin^de  track  trestles,  similar  to   E  and 

'   already  .lescribed.     They  differ,  however,  in  that 

.nn.I  II  have  a  ;{-foot  depth  <.f  earth  and  ballast 

nil  111  <r. 

Comparative  Trestle  Costs. 

The   comparativ."   eosts   for   the   foregointr   trestl- 
spans  for  both  sin-le  and  double  track  structures 
IS   fiivrn    un   the   eharl.    Fijr,,,,.   ,;,;.     The   horizontal 
ordinatcs    represent   clear  spans   in   feet,    while   the 
vertical   ordinates   give   the   eosts   in   dollars   for  a 
••""iplete    span,     not    including    piers.     This     chart 
'•I«'arly   sho^s   that   r-inforced   concrete   trestles   of 
the  types  marked  E  and  F  with  rod  reinforcement 
are  more  ■•conomical  than  any  other  form  of  pernui- 
i.ont  trestle,  with  solid  roadway.     The  chart  shows 
turther    that    reinforced    con-rete    railroad    trestle 
spans  of  slab  constructions  are  economical  fc  -ingle 
track  in  spans  up  to  M  feet,  and  for  double  track 
HI   spans   up   to   20    f,.,.t.      Above    these    lengths    the 
•H'onomic   form   of  span   is  a  combination   of  beam 
and  slab. 


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Comparative  Cost  of  Short  Span  Bridges. 


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IXDEX. 


Pago 

Abutments   ,'.">,  .",  148 

Movements  of  10 

lianklne's    Rules   fo*- 58 

Tiautwine's   Rules   lor 55 

Ahiitment   Piers   11,   54,   70 

Tiautwine's    Rules    lor 55 

Adda    River    Bridge 80 

Adhesion,    Concrete    to    Steel 

108,   114.  116.   l::6.  1N6 

Advantages   of   Masonry 1 

Aisne  River  Bridge 176 

Almendares,    Cuba    Bridge...   97 

Augustus,  Bridge  of 3,  75,  7ti 

Anthony    Kill    Bridge 97 

Anderson.    L.    W IHtt 

Approximate   Computations. .  32 

Aqueduct    of    Vejus Kiii 

Aicade — Spandrels      19 

Arch  Ring.  Thickness  of.  50,  51 

Architectural  Design   liio 

Area  of  Arch  Ring,  Required  ti9 
Atlantic  Highlands  Bridge.. 17< 
Atlanta.  Georgia.  Viaduct ..  .189 
Auckland.      N  e  w      Zealand, 

Bridge    80 

Austell.   Georgia,   Bridge 17S 

Austrian    Experiments    105 

Avranche,    Fiance,    Bridge.. 174 

Hacking   '2 

Tiakei's     Musonry     Constiuc- 

tion    ,',9.    :;is 

balustrade    1S7 

lUitter    of    Piers l.^.i) 

lUaring  Power  of  Soils .Mt 

I'.cllefiold  Bridge,  I'ittsburg.  IS 
Ho.im   Bridges    ISl,   IS.'] 

Advatitages   of    is:! 

Cost    of    1S5 

ppsign    of    i,K5 

landing  Monnrits    13:!.1.'!5 

Middle.    Col.    John S9 

Hinnie     96 

I'.ig      Muddy       ItiviT       Bridge 

17,    60,    S!t,    116 

i:if>me.    Rudolph    S Ifi3 

r.lock  Structures   7 

Hond.    Mechanical    lOS 

Con  ti'a  dors'    157 

liiiHton.     nridsre.s    in fi.'i 

I'.orrodale   Bridge    95 

liotmida   Bridge.   Italy 174 

Biisnla     176 

lioulder,  Col 17S 

24,'> 


Page 

Moulder   Fared   Bridge.    166.    168 
Brookslde    Park,    Cleveland..  97 

Brick   Arches    1 

Brick,    Strength    of 34 

Brooklyn,   Seeley  St.    Bridge.  176 

Brunei    30 

Brown,   Wm.   H 98 

Building   Lintels    5 

Burr,   Wm.   H...80,   147.   1.59.  179 

Bush.   Lincoln   96,  98 

Buda  Pesth  176 

Cain,  Prof.  Wm 128 

Carriage   Travel    Loads 123 

Cantilever,    Action    of 5 

Concrete    10 

Caius    Flavlus,    Bridge    Built 

by  74 

Casey.  E.   P.,  Architect.  .87,  159 

Canada  Creek   178 

Carter   98 

Cartersburg,  Ind 176 

Canal  Dover.   Ohio 176 

Cedar  Rapids,  Iowa 176 

Centers    7 

Chester   Bay    176 

Charley   Creek    178 

Chicago  Park  Bridge 169,   172 

Chatellerault,  France, 

Bridge    174 

Church.    Prof.    L    P 42 

Cincinnati    Park    Bridge 104 

Cleveland,  Rockv  River 

SI,   Sli,   83,   84,   95 

Colfax  Ave..   So.  Bend 176 

Columbia    Park     Lafayette. .  .178 

Courtwright,    P.   A 179 

Composition  of  Arclies 1 

Concrete    120 

Cost       of       Solid       Concrete 

Bridges   63 

Re-Concrete  150 

Slab  Bridges   183 

Beam     185 

Piers    1S3 

Conciete     Steel     Engineering 

Co 163 

Ccmo  Park,   St.   Paul 

F.I      ICa,    ICT,    17S 

Con.iugate  Pressures. .  .4,   si,  67 

Continuity  of  Arch 7 

Colonnade  Spandrels  19 

Compulations,  Approximate.,  32 


246 


II^'DEX 


Page 


i\\ 


Cooper'8  Engine  Loading. 
Connecticut' Av4;  "Bridge .\^"'  ""' 

Com^etiu:ei3.JgAiS**"-^%-;^ 
CorruKateil   nn-    *"'"«  101 


Bar 
Bridge/ 


-orrugated 
Craclis  . . , 
Cruft    St. 

olis   

TrlV."   ^'^"'^   <-''PPk 
(  rittenden,    H.    M 

Crown  Tlirust   . .  .'.V  "  aV 
Crown     rvf     A 1.  ••••••'^•'> 


118 

i- 107 

Ind  anap- 

ITS 

1 7.S 

...IT.-. 

40.   43 


-Arcli.,     Rise    and 


Crown    of 

Fall    

Thickness    .        

Radius    

Killing  Depth'oif!!!;:""i«" 

Cut^'lvn^f  of  Arch  Block.s/33"   ... 
£"*    ^^ater    on    Piers.....      'ir, 

Cunningham,  A.  O -- 

Culverts     ......       ■'' 

Req uired  open i ngs '  for .■.*;; 

Tables  of  .'.*.*.V'i,-,' "  -mit'  '  'wio" 
Cost  r'hnnt  •  -''•   -*'•>' 

Side 


10 
U 
].'. 
67 
34 


.i;.i 

.19!. 


Chart  ;;:.■;•. ::v;.:''r:ii] 


<'hart. 
•'orni.s  of. 


I'l; 
1-16 
217 
219 
S 


Walls    .... 
Comparative  Co.-t 
tomparntive    Co.«t 
Other  Common 

Curves  for 

Cu.shinn,  Filling  as. . .      ^l 

Cup  Bars ...::::; i}^ 

Danville  Bridge   .         -o'  „- 

iJanuhe  Hiver  Bridges.*." '  ""'   o-. 

iJayton,  Ohio V-Vi?;' 

l^es  Moines  Bri.lg...    " ""  V-"     -« 

&')":?:    I^'-'Jeerciev'e-''' 

Cost  of" ".'■".■.■  si' ■s'."8V'oV  ^i 

""iife"'...".'  -"c^'i : 

Design.    Ultra   Refinement  "  "     " 


Decatur   m.,   Bridge.:...      •'kb 

Decorah.  Iowa,   IJri,|g4 ]-c 

Derby.   Ponn.,   Bridge   i-« 

De  Mollins,    M    s^   ^'^ 

De  Palo.   Michael."."."""" 
Dock,    Kind   of . . 
D-'ck  Bridfies,  I'refei-ciu' 
Diversity  of  Design...  i. 

Diamond  Bars  .  ,]^ 


V, 

17,-. 

1 3.S 

e  for.lfis 


Douglas.  W.  J....S], 
Drainage  of  Arches. 


■  lis 

89,  IGG,  177 


Pa 


104,   1 

1 

1 


Duane.    W.   M gs 

Earth  Slopes  "    "     ' 

Eads    Bridge.    St." "  "louIs."  ." " " 
Koonomic  Span  Leiigtbs.. 
Edmonson  Ave.   Bridge 
Eden   Park.   Cincinnati     " 
Kla.stic  Theorv 
Electric   Car  Loads .".■.", 

Ellip.xe    

'I  o    Draw 

raiiptical    Intra(l"os i 

Emperor  Augustu.s  "." i 

Embankments,  Loads  from.. 

'^^Tmperger,"  "von  '."."."."iui  "  iVf''  J 
i'^mpirical   Rules    .  '         '  \i 

Emerlchsville  {: 

Kngine   Loading— ' 

Cooper's  E-50  . .  ., 

E.otimating   .  J 

European  Praeti'ce  ■.".■." ,' 

External  Loads  and  Forces'  '4    2 
r.xpan.«inn     .  x-un.es  »,  i 

Expan.sion   Joints".' i? 

Expanded   Metal    ..      \\ 

Kyach   River   Bridge. .'."." I 

Felgate,    a..    M.." ,:• 

Filling-Crown   .   ,    ""'• 

Load   froMi  

g;;^'p[j^Eiiipticai  "aVcVics."  : : ; : 

Finish,  Siirf;-ce 

i  ive      Centered      Ar(h,"""To 

Draw  

Merits  of 


11 

17! 

9t 

If 

30 
32 
32 

60 

22 

F.re  Insurance" ."  .".".■."." \\i 

Hoor  Renewals  9 

Huid  Pres.sure  t 

?,'-\V^'"^"^«---::::::::::::::io? 
Fieischmani-Eaward::::;::::;?^ 

Forms   ^ '  ° 

^!!l7l'I'"  o'  ^^Io«t  Suitable.   27 


Cost 

P'orees 


of 


.].-,4 


External   on 

Polygon  of   ■  ■  ■  QQ 

Foundations     .  ro 


.17 


.■is 


tions 
'•"crt,  E.  J 

Fort    .snelling,    Concrete   iV^. 

sign    o,,     ,-, 

Frankfort  Creelc  iiridge."."     '     97 

Iranklin  Brid;,'e.  F(.re.«ti'a'rk 

Funicular ' i-olyg :n'  '^!'^:.  .^.'^,-; . ^l] 


Page 
9S.   179 

tjuis.'.';;;n5 

?tlis i'30 

'S«^ 93 

't'--104,  178 
U'S 

m 

8 

20 

145 

••;■  •■.4.  76 
I  from. . 

5,     30 

Ji.  177,   179 

139 

174 

49 

1.-.4 

10 

orces  4,  29 

60 

148 

118 

97 

of —  n 

178 

C5,    90 

16 

30 

DS 32 

32 

60 

I,       To 

22 

Ho 

137 

2 

8 

107 

107 

fl8 

178 

8 

20 

table.  27 

1.-4 

29 

39 

58 

177 

.SO.    153 

97 

33 

i'»  rk 
Ifi-'.  178 
67 


fXDEX. 


247 


Pago 

i.alicia    Uridg..    iTc 

•.iirliHd     K-,,k     Hii.lij...  '  ('•iVi- 

'"•KO   J,;,;    .-., 

':-n.-i;il  Ouiliiif  s 

<;t  iinantowii  Hiidgf  j; , 

I Itiivial   Design   of  Ke-Con'<i'.    " 

Bndg.'s     ].,,; 

i.iis.l    Coiistniciion   Co  ici 

i.'uslatic    Aicli,    To    DraW  ] !  ! 

<  ;l.n(ioiii.    r'al!.'   iVridgV  '  "     '*'i  -v 
';"l<i«ii    (Jale    Park    Uii.ii-i.;; ." 

•  • fi],     ]ii4 

•.lanitf.   Strength   of....  m 

'ir.'.ri  Island.  Niagara  ...  .tiV  '  174 

i.iiicnwald   Rn    n\ 

<;nind  Hapids   Hiiig..'.;.'.'.      '  '^"' 

•  ••  • 106,    ](!!),    irb'  'i-,; 

Hrand  Hlvor   i-.'   ,-« 

'Iiaiid  Tower.   IW... '.'.["     an    n\ 
'J'Ti'I    Ave..    Milwaukee."       • 

„     119,  ij(!  ■]  r, 

Orern.   Prof.   Clins    K  ,-s 

<U\:\\n   Kivir    .  1-. 

Gwyiins  liiver '.'.'.'.'.'.  yc 

Hawgood.    Henrv    ...  01     09 

aiutuond.  .\.  j ::;■, .:i;.;{ 

ainsl.uig  HiiilKi.  .,- 

H.-iglit  of  Hii.K'.^.s  ■    ■■  ■    ','. 

H.adn.om    Iiider  Hridg,'s:  ]  ]   ^7; 
H'ywonh.   .;    (I..  I,-..    ; 

;i"^y:it.  w  >*  ...:::::::iw:\:^  * 

lI'rKinier,   X.    V    .  i-u 

HiMtje.s     '4 

ni"K<'d  .\r(  lu's  V.'ln'.'].'!).' ]i;o"],o 
istory  of  Cniierete  Bridges'    Kc' 

Kiu'li    Tension    St.,  |      .  .  ,,7 

ighway  n.am  HridK.  s.  ..■.";  .1  si 

'    '   '  "  .^'         1   -  Q 

Hihhard.    M.    s...  j-., 

Iliinliigton.    ind  i-'i 

Undsen   M(  morial   iiri'dge," ,' .' .'    ' 

!'nd^s:^,,   Kiv'.r  Hri.ige,   Sanily  '_  ' 

Ily,'rostati'o".\iell."ii,jw"lo'"' 
I  iraw   n    o,'    o- 

I'yle   I'ark  on   liuaaoiir.!."  !'i76 

|;]ahn.   -nridge    in ,9 

'"•    <"^"t.    i:.     1:.     liridKis.::.' 

Piandard   Culverts  •..,, 

:;|'h;.s   Uiver    nridge.    i;'nvi:{jh 

I'ier  River  Bridge.......   •).-,    ,    i    ' 

'i'lnaii.  Bavaria ''''r,-    I 

iMerlakcn,    MinncapoiiV!;  [liVs    , 


I  age 
Interme.liate  I'jir.s   ..  g, 

Iiiger.soll.    CM  S^ 

Intrado.s   Form    .  .' ] 1,^ 

Inzigliofen    Bridge        ,;'■; 

ln-lianapoli.s.  Moiri.s  hi.'  '.""\Yi 
Meridian  St.  .  ' '  i-w 
Illinois  St -J 

•  ■iiiit  St ; jij 

Northwestern   Ave  its 

lola.    Kan.sa.s    .    .  \-'^ 

lrrig.',ii,,n  Canal,  'in  "idaVio; !  u 
Isur  liivtr  Bridge 35 

Jark.oonville.  Florida.  BrIdgP  ITS 
Jaea.iuas  Uiv.r  Hridjj,.  '^  'i-, 
Jannstown       E  x  p  o  s  i  t  Ion 


T   „  '^'i'lge   .9.  Hill 

J.  ffer.v-on   St.,   South 


J^'liP.  B.  J    T..... 
Jouit.<.    i:.\|>ansion 

Ti  ii.sirin   in    

Judaun  


ii;i. 

Bend. . 
161,  lfi4, 


174 

174 

179 

148 

7 


Kahn,  Julins   179 

Kansas   Kiv;:..-.. '■'■''^'>^' \^'! 

l.alaniazoo  River  . 17s 

Keepers    ...  ,i? 

Kenipten    Bridge ' '. " '. '.  .."  r.'    JVl' 


Key   West.    Horida. . .  .  .  '07 

Ki.sHinger  Bridge   ''.'.".'  140 

97 


Kirehlieini    Bridgt 

Krcsno.   (Jalicia   ..,....'. . 

Taibaeh,  Austria 

I  ake    J'ark.    ililw.VuKi'e'  ' 

law  uf  I, ever.  .  . 

1  aiiiner    Av....     l-ittsiuug 

l.awreiieehurg    Trestle  '    -iq,') 

Kansing,  Mich -■ 

l-antra.li.   Cermatiy  n-, 

J-<fner.     B.     K iT-, 

Leonard,    John    B.  . .  "1-7 

T.englh  of  .Span.   KeononuVaY 

lea.   A.    B 

1.1  ihlirand.  Max    . 
l-iiidenthal   Custav 

lima.    Ohio    

1  i<|iiid   Pressure  . . 

lintels    r 

line  of  Ifesistane-.  IndViinii'.'     7 
I  iet(  rinination  of  ■•(; 

I'osition  (.f  \ ;,;, 

Fi'r   Filiform   T.onil j" 

lor  I'aiMal  Load   :.-," '  ^^>^<^ 

Linear  Anii    ^^    ..vj 

Limestone.    Strength    1  f .  .      '   Tu 
Liability    Insiiranee  1-7 

I>ogar.sport.  ind. its 

London,    (Jliio 178 


W 


176 

174 
171 

i:;i 
97 


];? 

!  S 
ITT 
ITS 


I 


[I 

ft  1. 

1 


m  I 


2-18 


IXDEX. 


_    '  Vnifo 

Loire   River   i-i 

Loral  l.abor '.    M 

Loads    ]' J  .jf 

Load.   Contour  UtduVtVl 41 

Adjustini-nt    to    Form    '    "'    ]■) 

Kxternal     ' ' '   .iIi 

rnp\pn   .' ,"o 

On  t'ulvcrts .A'.K, 

LonK  Koy  Viaduct...        0: 

'•'"<'"•  f).  li K."..  ■iV7,'lV:t 


'i'r  u.s.s 


.lis 


T.utf>n".s   Kiiipirical    Kornvilii     -'I 

Luxemburg  j,o,  ill 

Mary  RIvpr   17s 

MaryborouKh   l?ridK'-   ITS 

Maumee   Rivor    Uridgc...      "iji; 

Marsii    Bridge   Co j;; 

Maintenance •» 

Ma.sonry.    Strength  of.'.','."  g 

Matliriiiatlcal        Theory        of 

Arcli ^2 

Materials.   Strength   of...  ^A 

Maracliina   River,    Ilalv 76 

M:iin  River ",  117 

Main  Street  Rridpc,  bavioii'l'Tf; 
Mclntyre.    Ch;irlf.«    ...   '  ];') 

Melon.    I'rnf.   j 1113  "17:, 

Merit.s  of  Concrete  Uridgis!. 

]07_  ](U 

Metal  Reinforcement 1 1 1 

Medium   Steel    "m 

Meyer's  Formula ]'.i\ 

Mechanicsville  Bridge '   !)7 

Mercereau   17;) 

Milwaukee  Viaduct  '. . .  .]]'.i 

Milteriliurg    (('7 

Missi.«.sippi    River    '.'.'.'."  it; 

Middle  Third  of  Arch  Ring..     ;!:! 

Miners   Ford    17s 

Mis.sion    Ave.,    Spokane. ...!' ITS 

Miami  151  vor 174    ]7(; 

Monroe  St.   Bridge,    Spokane    7> 

Mois.seiff,   T<.    S so 

Morsch.  Prof.  ,j si    !n; 

Morrl.son.  fleorge  S so'  in; 

Monier,    .lean    'lo:! 

Morris    St..    Indian;'polis. ..'."!] 71 

Monolith  Frame  ^s 

Murray.   Paul  R 177 

Miiltl-<^enter  Curve 9 

To  Draw 21'.   '"i 

Municipal   Art  League '  fs 

Mundt'i'kingt  n  15 

Navier's  Prlnci.    :.  04 

National   Zonlogical   Park!!..'  fil 

New    York     Riidges 7; 

New    Zealand.    Longest    Mi- 
sonry  Span    80 


I'agi 

Neckar  River  gi 

Bridge     '  3 

Nelson   St.    Viaduct.    A'tian'ta!l!s! 

Newark,    N.    J n 

New    (jushen,     Ohio 171 

Newton,  Ralph   K !!i7. 

Neckarhausen,  Germanv  t 

Niagara  Falls,  Green  Islati.i.. 

...    til,   171 

.Min<s,    Aiiiiedu'^t.     Krance.  .  .]ii; 

Noi.^e,  Absence  of 11,7 

Northern    Pacific   R.    R.    Cul- 
verts      "•10 

Nobel,  Alfred !!!!!!!!!!  "os 

Oconomowoo,  ■\:^'fs    i7<j 

Olive  Ave.    Bridge,   Spokan'e'.!l7s 

<^>pen   Spandrels    i; 

Ornamental    Bridges    !!!!  '>C 

O.xhcirn.     Frank    c "l7'' 

Outline,   General   ...luij 

Parkhiirst,  H.  W ni    H 

Park  Bridge  Design '   <i'\ 

Pantheon,   Rome    !!inii 

Painting     • 

Painting   Reinforcing   Steei!!ii6 
Parabolic  Arch,  To  Draw 

„       • -■!,    l!l.    117 

Pavement    jt; 

I'avement    Slabs    !!!!'''l.", 

Paveinent  Tics   '"-,«! 

Paulins    Kill    07 

Painsville.  Ohio   ']',4 

Palerson.   N.   J KU 

Plainwell.    Michigan    !!"l7s 

Passaic   FSiv  er    17(5 

J'arlial   Load.    Line  of  i'ress- 

U'e   i.-,,   6s 

Peoria  Bridge    140 

I'elham    I'.ridg'    !!        "i7fi 

J'eru.  liid..  Bridge I7i; 

Pena    River    174 

Philadelphia   8."),   86,    S7    9.". 

Philadelphia,    Tacoiiy    Creek.    !i7 

I'iney  Creek    18,   !<; 

Piers.  Thickness  of..i;6    IP 

c.  St  of  ' 

-   hutment    li,    .-4 

Intermediate  '.   53 

I'ier  Thrust.    To    Balance....'  14 

J'me    Creek     17s 

Pittsburg.    Pa 07 

Piles.    Batter   and   Plum-,!      !  5:1 

l.iiad    on     

Pla.va    Del    Riv.. 
Plaintield.    Ind.     . 
Pl.Tuon.    Germanv    ...        sii 
I'otoniac  MeiiKnial   Bridge   !'. 
117,    I." 


112 

l.-ii 

.IS! 

711 

61) 


.->9 
.171 

.178 

8" 


iri9 


Ri\er 87 


ixnr.x. 


240 


r'agp 

85 

!):. 

Ulanta.1.v<» 
m 

iTi; 

17.-. 

ii.v  ....  H.") 
slaiiil. . 

...til,  171 
lllcr.  . .  iiir, 

107 

t.    Ciil- 

17.S 

)kanf'..17s 

17 

no 

17:' 

lull 

ni,   H 

!i:i 

in.i 

3tori.'.'ll6 
iw.  . . . 
.   lU,   1(7 

16 

2\:> 

.'.6 

07 

IVJ 

I7ii 

17S 

176 

'rcss- 
...1.'..   6.S 

140 

176 

176 

174 

6,    S7,    9.'i 

rook.   !t7 

,   !'7.   142 

II v.   l.-.ii 

IS;! 

I,    .■>4.    711 
...53,  6n 

!e 14 

17S 

.      .   97 
......   5!t 

59 

i;4 

178 

..SU,    8'. 

!:•:;,  1.-.9 
87 


Pajjo 

I'ortland.   Pa.,  Bridge '■>:> 

I'oilo    Uk'o     174,    17.S 

I'urtugul     174 

I'ollii.sKy.   Cal 176 

I'uiit    l>u    tJard lo,') 

I'oiitf  ItDtUt.  Uuiiit' ;>,  ',o,  74 

I'oiis  AciMllius 74 

ralalimis   74 

La|iiilt'iis    74 

rolynon,  Koicf  ;t9 

I'ulo    39.   67 

Ui.stanc'f    4;{ 

roiiil    of    Uiiptui-f .".0 

I'lt's.suif  Curve,  To  Deter- 
mine         ofi 

ProKKuie    of    Liquid 5 

Sand    5 

Pressure     on      Surface.s,      'I'o 

Find     4.' 

Prlees,    Ksti^natlng   17,:, 

I'leservation   of   Steel 114 

I'yriniont.   France   174 

Quitnliy,    Honry    M S7,   9S 

Quantities.  Approximate   1.'.8 

Railing    187 

Halslun,  J.  (' 179 

Uankine's  lUiles  for  Crown 
'l"liicl<ne.ss    14 

Pier    'Pliickno.5s    .").'!.    66 

Rankine's  Motliod  of  Draw- 
ing H.\drostatic  Curve.. 
26.  27 

Rules  for    \butment  Thick- 
ness        58 

Railroad     Bridges 2.    ,1 

Roiiifoiced    Concrete    ,\rc'ies, 

^os^s      1,",0 

Tal.le    of    

..174,    175.    17i;,    177.    17S,    17H 

Part  II    1(10 

A<l\antUBes     of      Iu6 

Reynolds     175 

Reduced     Load    Contour 41 

Reilly    and     Riddle 87 

Reinffrring    Stool 101,    111 

Rein'orcing     Systems     117 

fietaining   Wails    122 

Rlione    JUver     174 

Riverside,   Cal,   91,   92,   93,   94.   97 

lllboud     177 

Ricluiiond,   Va.,   Trestle  154.   ISS 

Rise    of    Arch 8.    40.    66 

Rise    and    Span 12 

Rihbed    Arch 129.    142 

Ro^k vllle    .Stone     Arch 61 

Roxhorongh.     Pa 87 

Rocky   River   Bridge.   Cost   of 

64.    9.5,    80,    81,    82.   83,    84 

Rotation    of    Arch    Blocks..  33 


Page 

Rock    Skewbacks     2!> 

Rock    Creek     S7,    176 

Rome,    Ponle    Kolto....3.    73,    74 

Roman     Arches     8 

Length     of     Spans 

13,     i3,     i4,     to,     76 

Rusche,    J.    1' 16H 

Rupture,     Point     of 5u 

Santa    Ana    iiiidge.    Cal 

55,     91,     92,     93,     94.     97 

Sun    Uubriel    River    Hridge..l7s 

San    Joaquim    Kiver 176 

San     Francisco     Bridges 61 

Sangamon    River    176 

Sandy    Hill,    X.    Y 153,    178 

Sarajero,    Bosnia     176 

St,     I'aul     Bridges     174 

St.    Josepli    Kiver 174 

St.     Louis,     Kads     Bridge 145 

Sand    I'ressure     5 

Sandstone.     Strenglli    of 34 

Scolleld     Engineering    Co.... 

161,     175 

Sdiillinger    Bros 85 

Seeley    St.    Bridge,    Brooklyn. 176 

Schenley     Park     Bridge 18 

Schefflers    Theoroni 32 

Semi-Circular    Arch    8 

Senators'    Bridge    74 

Segmental    Arches     f» 

Culvert     Arches     14 

Selection     of     Most     Suitable 

Form     27 

Sewer    Arch     32 

Simpson  and  Wilson,  Engi- 
neers        96 

Sitter    River    81 

Skew-back,    Rock     28 

Slab    Table    for    Culverts 198 

Slabs,     Cost     of 200 

Slab    Reinforcing    118 

Slab    Arches    129 

Slab      Bridges,      Table      with 

Costs     183 

Slab    and    Beam    Bridges 198 

Slopes,     Earth     5 

Sliding   of   Blocks 33 

South    Bend.    Ind 174 

S' issoins.     France     176 

Solid    Arches,    Tables    of 

95.   96.   97,   98 

Soil,    Bearing    Power    of 59 

Spokane,     Mission    Ave 178 

Olive    Ave 17s 

Kiver     178 

Monroe    St 79,    72,    97 

Spandrels    147,    16,    17 

Spandrel    Columns     138 


2:.o 


ixnr.x. 


■ 


»p1 

Hi:  If 


VlVr 

Col- 


a; 
M 
!t:. 


Spancinls.     Arcade     or 

'iiiiiadf    

Spi.iirifi    Killing    .....!!!   28 

S|).  iiiKs.    l.ovv    

I'lisiii.iri    of    

Kpari 

Spirylrn    Idivvn'  CreH<  ' '  '.TS. 
Stii;  y      Cruok      Uridgc.      l;„.s- 

^.      '""      fi.'i 

M '•>!•.    Austria     n,-,_    174 

Slahillly     ItciiniicltlfntH.  .as'    13(i 

Sti.ckliridKc     Mass '     176 

Stt  ln-'r.iif<n    UridKi-    17;; 

Stc<>l     UcihliircijH  lit     ,.101      in 
Strt'iiBth       of       !{<•-( '(incrtto 

„,,   '^'•'•'"•s     10: 

Stirrups     117 

Siir\«y     for     MiidKc  .'.'.'.'.■.■.'■  ■i.-,7 

Siirfacf     Kiiiisli     '   (•,„ 

Switzerland    Hridgc     ..'.'.'.'.'.[  m 

Tafony    rit-ek    07 

TeltiilKinf    at    nridgc .'.".'.'         i-,7 

Terr.-    Haiito     ....  [is 

Test     Loads     1 

Tf-nsion    in    Joints 7 

Tension    in    CoiKietf. .  114 

Teiifen     Uridij...     Switzerland  1T:1 
I  enipeialllle    Stresses 
Tliickliess    of    .\r<li 
'J'iiehps     Mrldge     .    . 

Tliaiiies     Hiver     liiidKe 'i", 

Ttiaeher.     Kdwiii Is,    ll'i    "177 

I  haeher    Har.s     '     us 

Three      fentered      Aieli   '  '  'I'o 

I 'raw     oi, 

Merits     of     '.'.'.'.u:, 

Theory,     Matlieina t leal  '  n- 

I  lieory    of    .Arches.,,.  '  1% 

Thrust      on       piers.       Tnhai- 
anced     -•> 

Ties    on     Bridge     KInor.s,  ,    '   107 

Ties.     Pavement  -<; 

Tiher    River,    itonie 74 

Topelja    Bridge,    10,    .li,    H9']7i 

Trestles    ,  , 

Eennnniir     Spans 
Rail    Tops,. 
Ream   'r,,p>t 

Str..|     R.nill 

Riiiiii    Tops 

^     '    Reiiiforei 


ll'i, 
lilnyr,,. 


ir.u 
r;.". 


Ill 


.  2.10. 
ks','.' 


,T'!1, 


22.S 


Slabs,    Rod 

Rod 


2:! I,  2:;:. 
■;<;.  23S 
•iiii'iit. 

n.'inis.        Rod        U.iiiforee- 

nient    o-'s     o.>9 

foniparativp    Costs  '    'm'-"' 

Chart     ..,.■.■.  ■.■.L'lS 

T^rtiporarv     ,  ,  ,  .  4s 

Trinidad,    Col.  i-u 

Trim    Creek    '.'.'.'.'.'.'.'.'.'.l^S 


Truss  System  . . , 
Ttautwines  ijulc 
Thifkness  . . 
Aliiitliieni  I'iers 
Travertine.  IscU 
Trial  Metliod  of 
'i'uliesing,     w      |.- 

Til  sea  I  a  was     Uiver 


for  Crown 


in  UoiiK 
iHsign , , , 
I«:i, 


.1; 


I II 


Turner.  K.  Al . . 
'I'uriier.  ('.  A  I' 
Tunnel    Areh    .', 

Twisted     Rods     ,        

Twist,  d    Lug    IJars ,'.'.'■.' 

T^V'-'ll.       II.       n..       Coneiet.' 


.11 
17 
1: 
17 
17 

11 
11; 


HrldK 


ii; 


u 


3:i 


designed    hy 

_  Is.    (JJ.'   Mil 

T.vrrell,       M.       K..       Designs 

'•>    I,s.'.   is 

rUra-Reflnement    in    Design 

'.innate   Values    "       ,. 

1  Im,    (Jernianv    , ,  ,  9" 

Ijieertalnty    o"f    Masonrj  "4 '   r.^ 
I   nit     I'lessiires  '       " 

On    Surface.    To  '  Fi'n.l 

>\  orkitig     

ritiniaic    an  j'    WoVking. .' .'  p";, 
T  nit     Reinforcing    l-Yame,  .  ,  ,  Us 

l.iiev.ri    Ijia.ling    ,'s 

«-Jlsyninu!i  i(  al     Alcli     ...... l'i\i 

y.nrloiis   Po-ms.    To   Draw.,     "(i 

\  allies,      ritilliate      ,  •;( 

\ar.Mn^  Span    Lengths    13 

\aiixliall,     London     ,..  «(", 

\ein,iiii„„         jjiv.         Bridge' 

Wakeinan    9.    .jo,    174 

\  •rmillion   Riv.    Bridge,   nnji- 

ville    72    97 

Vo.fns.     Aqueduct    of ..    "int'i 

\enice.     Cal i,;9      \-] 

Viaducts    over    Yards ']:!     6fi 

\iIiiation.     Absence    of.  107 

\  iiime     Rixer     174 

Von    K'inperger    ,    ..104,    177,  "179 
■V^'.nshington,      n.      C.      Rock 

,,  ''••'••■k     I7fi 

(  onneclicut     Avi>, 

„.     ■• S7,    SS,    ]i:(i,']fiS 

\Jnsliington    St..    Davtnn. . .  .17t; 
Waleilfxi,    Iowa     .,..".  17S 

A\ahnslK    Ind i 40.    ns 

Mat.'rvllle,     Ohio     ...  17(; 

Wavne    St..    Peru.    Ind.  .'.■.'.■.■  J  7f. 
\\  alker     j  — 

Wakemen.    Ohio'  '.'.■.'.'.'.■9"^o'  'lU 
\^n,.*.     Thickness    of    Span- 

<lrel     J  3 

Loads    on    ....         09 

Waterproofing    '.'.^'.'.52,'  '2I6 


"     f:! 


j.\i)i:.\. 


•2ol 


PttK- 

^ 

•  Crown 

n 

Uonif.  7) 
^iKi".  ...in; 
.  ..Ui;i,    177 

174 

■•IT.-',    J  77 
...lU.  17.-. 


ilng. .  .11'.-, 

mo n^ 

IIS 

13i' 

raw...  2<i 

,".  t 

13 

;i.", 

Jrklge, 
>.    .10,    174 

I'nji- 

..  .72.   97 

106 

.1«9,    171 
...1.'?.    66 

107 

174 

177,    179 

Rock 
176 

ii';(i."'i6,s 

n 176 

....   17S 
110.    17S 

176 

176 

177 

P.O.    174 
!pan- 

19 

29 

.52,    216 


Page 

Watersoaklng   no    U.'. 

Waterway.    Width    of &G 

Walnut     l.ane     Uridge,     Sur- 

faco    Kiniitli    60 

Co.st   of    64.    14J,    SO,    85,   97. 

Warren.    Whitney.    Arehltect.   S" 

Wat.son.    Wllber  J s,',,   17.-, 

Waldhofen     174 

Wells.     W.     H 179 

WehBter.    George    S,,85,     96.    9s 

Whited,    Willis    9H 

WlldegK.    Switzerland 174 

Wise,    C.    H 177 

Wilson,    George    I, 179 

Wideniug    Concrete    Bridges.     3 


Page 
Window   Arches,    Load  on...     6 

Wire   Net    Heinforcement 118 

Width     ul    Deik 138 

Wing    Walls    149 

Wlssahiclton   Creek    95 

Wurknianslilp    7,   no 

Working  Units   35,   106 

Wood     Bridges,     Competition 

with     102 

Wunsch.    Professor    116,    177 

Wyoming      Ave.,       Philadel- 
phia        97 

Yellowstone    Park    Bridge... 174 
Zeslgtir,   A.   W 98 


A 


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and  other  books  for  Kngineers  and  Contractors.  lingineer- 
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Mr.  Gillette  has  just  completed  his  appraisal  of  all  the  rail- 
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Hy  HALBERT  P.  GILLETTB 

and 

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This  book  is  unique  among  all  the  books  on 
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forms  and  centers  and  the  layout  of  plant  for 
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Concrete 

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Theory  and  Design 

OF 

Reinforced    Concrete   Arches 

A  Treatise  for  Eni^inecrs  and  Technical 
Students. 

hy  ARVID  REUTERDAHL,  Sc.  Ii...\.  M 

Chief  of  Briiigc  Depart  iTiiMit ,  Bn^inccrinR  fX.parlmciit, 

City  i)f  Spcikiiiic,  Wash. 

The  books  wbicli  li;ive  heretofore  been 
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niathematicLilly  abstruse  or  leave  s'> 
much  to  the  reader  to  demonstrate  for 
liimself,  that  they  are  of  little  value  to 
the  general  practitioner  or  to  the  tech- 
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there  are  no  missing  steps  in  (he  niathe= 
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By  ERNEST  McCLLLOUGH,  C.  E. 

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worker — the  man  on  the  job — who  has  not  the  re- 
quirements of  statics  and  the  theories  of  the  mathe- 
matician at  his  tonj,'ue's  tip  but  who  desires,  in 
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Hy  FRANK  IV  OILT?RETH 

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growth of  over  twenty  years  of  experience  in  the 
contracting  business,  and  embodies  scores  of  sug- 
gestions for  i'conomizing  and  for  increasing  the  ou'- 
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tractor who  made  the  "("ost-plus-a-fixed-sum-con- 
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famous  Gilbreth's  "Fitld  Systeni,"  only  a  few  ex- 
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thousand   lOpvf- 


One 

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In  making  pnbln.  >us 
\  ,  pi  rforniing  a  sei  \  U  i 
parabU-  w  Uh  the  ;u  ti- 


re sold  in   the  first  ten 


Field  S\  ,tem"  Mr.  (Iilbreth 

I.      the   pul)lic   that  is  com- 

'\  a  physician  in  disclosing 

the   svtut   (if   his  sv\\  V  v  >>,  in  curing   a   disease.      The 

dtHcaso  that  Gilbreth  s  "Field  Sv--tem"  aims  to  cure 

is  the  hit  'V  miss  methoil  ot   doing  contract  work. 

Svstem  supplants  slo\  i-nliness,  and  makes  sloth  an 

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